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Equations Review #1, Systems of Equations Word Problems

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12, 8

A boat traveled 160 miles downstream and back. The trip downstream took 8 hours. The trip back took 40 hours. What is the speed of the boat in still water? What is the speed of the current?

16, 7

A boat traveled 207 miles downstream and back. The trip downstream took 9 hours. The trip back took 23 hours. What is the speed of the boat in still water? What is the speed of the current?

20, 4

A boat traveled 336 miles downstream and back. The trip downstream took 14 hours. The trip back took 21 hours. What is the speed of the boat in still water What is the speed of the current?

15, 7

A boat traveled 88 miles downstream and back. The trip downstream took 4 hours. The trip back took 11 hours. Find the speed of the boat in still water and the speed of the current.

8, 8

A coffee shop is having a sale on prepackaged coffee and tea. Yesterday they sold 40 packages of coffee and 25 packages of tea, for which customers paid a total of $520. The day before, 40 packages of coffee and 50 packages of tea was sold, which brought in a total of $720. How much does each package cost?

origin

(0,0)

3608, 328

A company that teaches self-improvement seminars is holding one of its seminars in Brookfield. The company pays a flat fee of $328 to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend $10 to purchase books and supplies. Each attendee will pay $11 for the seminar. Once a certain number of attendee register, the company will be breaking even. What will be the company's total expenses and revenues? How many attendees will that take?

11, 33

A customer at the mall is shopping for holiday gifts, and is considering having them wrapped. He can get them wrapped at the department store, which charges $3 per gift. Alternatively, the customer can pay his niece a flat fee of $33 to wrap all of his gifts. If he has a certain number of small packages, it would cost the same amount either way. How many small gifts would that include? What would be the total cost to have all the gifts wrapped?

130, 13

A plane traveled 1287 miles to Lagos and back. The trip there was with the wind. It took 9 hours. The trip back was into the wind. The trip back took 11 hours. Find the speed of the plane in still air and the speed of the wind.

100, 25

A plane traveled 1500 miles to Paris and back. The trip there was with the wind. It took 12 hours. The trip back was into the wind. The trip back took 20 hours. Find the speed of the plane in still air and the speed of the wind.

75, 25

A plane traveled 600 miles to Tokyo and back. The trip there was with the wind. It took 6 hours. The trip back was into the wind. The trip back took 12 hours. Find the speed of the plane in still air and the speed of the wind.

66, 22

A plane traveled 880 miles to Chicago and back. The trip there was with the wind. It took 10 hours. The trip back was into the wind. The trip back took 20 hours. Find the speed of the plane in still air and the speed of the wind.

slope

A ratio comparing the change in output over the change in input of a line. The steepness of a line.

6, 14

An employee at an organic food store is assembling gift baskets for a display. Using wicker baskets, the employee assembled 5 small baskets and 10 large baskets, using a total of 170 pieces of fruit. Using wire baskets, the employee assembled 6 small baskets and 10 large baskets, using a total of 176 pieces of fruit. Assuming that each small basket includes the same amount of fruit, as does every large basket, how many pieces are in each?

linear equation

An equation in two variables whose graph in a coordinate plane is a straight line.

24, 46

An event organizer is reserving rooms for two company-wide events. For the quarterly meeting this month, she reserved 5 conference rooms and 5 ballrooms, which can seat a total of 350 attendees. For safety training next month, she reserved 1 conference room and 5 ballrooms, which can seat 254 attendees. How many attendees can each room accommodate?

78, 144

An event planner routinely orders ice sculptures for the corporate events she plans. For an executive dinner in Stafford, she ordered 5 small ice sculptures and 1 large ice sculpture, which cost $534. Then, for a release party in Middletown, she ordered 1 small ice sculpture and 1 large ice sculpture, which cost a total of $222. How much does each ice sculpture cost?

14, $68

Aunt Kate is pricing cakes for a baby shower she is throwing. She wants one large cake shaped like a duckling and also some cupcakes in pastel colors. Belmont Bakery charges $3 for each cupcake, plus $26 for the large cake. Albert's Sweet Shoppe charges $54 for the large cake and $1 for each cupcake. If Aunt Kate orders a certain number of cupcakes, the cost will be the same at either bakery. How many cupcakes would that include? What would the total cost be?

9, 5

Bill and Molly each improved their yards by planting rose bushes and ivy. They bought their supplies from the same store. Bill spent $102 on 8 rose bushes and 6 pots of ivy. Molly spent $97 on 8 rose bushes and 5 pots of ivy. What is the cost of one rose bush and the cost of one pot of ivy?

10, 6

Carlos and Chelsea each improved their yards by planting grass sod and ornamental grass. They bought their supplies from the same store. Carlos spent $206 on 14 ft² of grass sod and 11 bunches of ornamental grass. Chelsea spent $136 on 7 ft² of grass sod and 11 bunches of ornamental grass. What is the cost of one ft² of grass sod and the cost of one bunch of ornamental grass?

9, 11

Danielle and Dan each improved their yards by planting hostas and geraniums. They bought their supplies from the same store. Danielle spent $231 on 11 hostas and 12 geraniums. Dan spent $186 on 6 hostas and 12 geraniums. What is the cost of one hosta and the cost of one geranium?

55, 19

Dr. Howell, a pediatrician, has 2 annual checkups and 2 sick visits scheduled next Tuesday, which will fill a total of 148 minutes on her schedule. Next Wednesday, she has 1 annual checkup and 3 sick visits on the schedule, which should take 112 minutes. How much time is allotted for each type of appointment?

172, 40

Flying to Cleveland with a tailwind a plane averaged 212 mph. On the return trip the plane only averaged 132 mph while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.

191, 13

Flying to Tokyo with a tailwind a plane averaged 204 km/h. On the return trip the plane only averaged 178 km/h while flying back into the same wind. Find the speed of the plane in still air and the speed of the wind.

103, 27

Flying with the wind a plane went 130 km/h. Flying into the same wind the plane only went 76 km/h. What is the speed of the wind? How fast would the plane go if there were no wind?

140, 13

Flying with the wind a plane went 153 km/h. Flying into the same wind the plane only went 127 km/h. Find the speed of the wind and the speed of the plane in still air.

308, 34

Flying with the wind a plane went 342 mph. Flying into the same wind the plane only went 274 mph. Find the speed of the wind and the speed of the plane in still air.

slope-intercept form

Form for a linear equation: y = mx + b

point-slope form

Form of a linear equation: y-y1=m(x-x1)

33, 2

Gwen flew home from vacation with a heavy bag. With the first airline she flew, Gwen had to pay $25 to check her bag, plus $4 for every pound that her bag was over the weight limit. The next flight was with another airline that had the same weight limit. Gwen had to pay $5 per pound that her bag was over the weight limit, in addition to the checked bag fee of $23. By coincidence, the fees ended up being the same with both airlines. How large was each airline's fee? How far over the weight limit was the bag?

11, 48

Isaac and his friends like to collect and trade cards from a certain combat card game. Isaac used his allowance to purchase 8 booster packs and 2 premade decks, which included a total of 184 cards. For his birthday, he received 1 booster pack and 2 premade decks, which included a total of 107 cards. How many cards come in every booster pack and every premade deck?

11, 4

Jacob and Kali each improved their yards by planting grass sod and shrubs. They bought their supplies from the same store. Jacob spent $123 on 9 ft² of grass sod and 6 shrubs. Kali spent $125 on 7 ft² of grass sod and 12 shrubs. Find the cost of one ft² of grass sod and the cost of one shrub.

8, 53

Jenna and Neil, the boy she was babysitting, were playing basketball together. Her score was 29 points, and his score was 13 points. Jenna wanted to make the game more fair, so she called a time-out and modified the rules a bit. Jenna explained that, for the rest of the game, she would get 3 points per basket, and Neil would get 5 points per basket. Then they played a bit longer. After the time-out, they both made the same number of baskets and ended up with a tied score. How many baskets did each person make after the time out? How many points did each person have at the end?

14, 20

Jill and Paul are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Jill sold 4 small boxes of oranges and 5 large boxes of oranges for a total of $156. Paul sold 7 small boxes of oranges and 9 large boxes of oranges for a total of $278. Find the cost each of one small box of oranges and one large box of oranges.

48, 6

Jonah wants to make scrapbooks with old family photos. An online scrapbooking company charges $42 for a basic book and $1 per page. Meanwhile, a family friend is willing to make a scrapbook for $30 plus $3 per page. For a certain number of pages, the price would be equal. How much would that cost? How many pages would that be?

28, 149

Last Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Hayley can read 2 pages per minute, and she had already read 93 pages. Akash, who has a reading speed of 4 pages per minute, had read 37 pages. Eventually they had read the same number of pages. How long did that take? How many pages had each of them read?

y = x + 2

Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?

Line CD passes through points C(1, 3) and D(4, -3). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?

-21

Line JK passes through points J(-4, -5) and K(-6, 3). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?

35, 16

Lisa and Vivian are hosting events that are catered by the same company. Lisa plans to have 77 adults and 32 children attend, so the total projected cost of her meals is $3,207. Vivian has 97 adults and 32 children on her guest list, so she will pay the caterer $3,907. How much does the caterer charge for each meal?

7, 10

The sum of two numbers is 17. Their difference is 3. Find the numbers.

6, 8

Mark and Scott are selling pies for a school fundraiser. Customers can buy apple pies and lemon meringue pies. Mark sold 4 apple pies and 11 lemon meringue pies for a total of $112. Scott sold 3 apple pies and 14 lemon meringue pies for a total of $130. What is the cost each of one apple pie and one lemon meringue pie?

12, 3

Micaela and Brenda each improved their yards by planting daylilies and ornamental grass. They bought their supplies from the same store. Micaela spent $87 on 4 daylilies and 13 bunches of ornamental grass. Brenda spent $201 on 14 daylilies and 11 bunches of ornamental grass. Find the cost of one daylily and the cost of one bunch of ornamental grass.

546, 6

Nick, an artist, plans to paint and sell some miniature paintings. He just bought some brushes for $60, and paint and canvas for each painting costs $81; he will sell each painting for $91. Once Nick sells a certain number of his paintings, he will be breaking even. How much will Nick have earned? How many paintings will that be?

6, 4

Norachai's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 5 adult tickets and 9 student tickets for a total of $66. The school took in $60 on the second day by selling 8 adult tickets and 3 student tickets. Find the price of an adult ticket and the price of a student ticket.

3, 11

Rob and Ryan each improved their yards by planting rose bushes and ivy. They bought their supplies from the same store. Rob spent $135 on 12 rose bushes and 9 pots of ivy. Ryan spent $145 on 8 rose bushes and 11 pots of ivy. What is the cost of one rose bush and the cost of one pot of ivy?

10, 7

Sarawong and Jack each improved their yards by planting hostas and shrubs. They bought their supplies from the same store. Sarawong spent $69 on 2 hostas and 7 shrubs. Jack spent $95 on 6 hostas and 5 shrubs. What is the cost of one hosta and the cost of one shrub?

8, 15

Shayna and Jessica are selling pies for a school fundraiser. Customers can buy blueberry pies and blackberry pies. Shayna sold 2 blueberry pies and 12 blackberry pies for a total of $196. Jessica sold 12 blueberry pies and 12 blackberry pies for a total of $276. What is the cost each of one blueberry pie and one blackberry pie?

4, 1

Suzie gets paid at home for doing extra chores. Last week, she did 2 loads of laundry and 9 loads of dishes, and her parents paid her $17. The week before, she finished 1 load of laundry and 9 loads of dishes, earning a total of $13. How much does Suzie earn for completing each type of chore?

12, 13

The difference of two numbers is 1. Their sum is 25. Find the numbers.

7, 11

The difference of two numbers is 4. Their sum is 18. Find the numbers.

y = 1/4x + 2

The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y - 4 = 1/4 (x - 8). What is the slope-intercept form of the equation for this line?

x-4y=8

The point-slope form of the equation of the line that passes through (-4, -3) and (12, 1) is y - 1 =1/4 (x - 12). What is the standard form of the equation for this line?

2x + 5y = -15

The point-slope form of the equation of the line that passes through (-5, -1) and (10, -7) is y + 7 = 2/5(x - 10). What is the standard form of the equation for this line?

y = 1/2x + 2 1/2

The point-slope form of the equation of the line that passes through (-9, -2) and (1, 3) is y - 3 = 1/2 (x - 1). What is the slope-intercept form of the equation for this line?

3, 13

The school that Alberto goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 12 adult tickets and 8 child tickets for a total of $140. The school took in $138 on the second day by selling 7 adult tickets and 9 child tickets. Find the price of an adult ticket and the price of a child ticket.

9, 8

The school that Asanji goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold 11 adult tickets and 3 child tickets for a total of $123. The school took in $187 on the second day by selling 11 adult tickets and 11 child tickets. Find the price of an adult ticket and the price of a child ticket.

3, 5

The school that Mike goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 10 senior citizen tickets and 3 child tickets for a total of $45. The school took in $92 on the second day by selling 9 senior citizen tickets and 13 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

3, 15

The school that Ndiba goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold 1 senior citizen ticket and 13 child tickets for a total of $198. The school took in $201 on the second day by selling 12 senior citizen tickets and 11 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

5, 15

The school that Ndiba goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold 13 adult tickets and 12 child tickets for a total of $245. The school took in $225 on the second day by selling 9 adult tickets and 12 child tickets. What is the price each of one adult ticket and one child ticket?

3, 10

The school that Paul goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold 7 senior citizen tickets and 1 child ticket for a total of $31. The school took in $182 on the second day by selling 14 senior citizen tickets and 14 child tickets. What is the price each of one senior citizen ticket and one child ticket?

5, 5

The school that Ryan goes to is selling tickets to a spring musical. On the first day of ticket sales the school sold 14 adult tickets and 2 student tickets for a total of $80. The school took in $95 on the second day by selling 14 adult tickets and 5 student tickets. What is the price each of one adult ticket and one student ticket?

13, 23

The senior classes at High School A and High School B planned separate trips to Yellowstone National Park. The senior class at High School A rented and filled 4 vans and 3 buses with 121 students. High School B rented and filled 4 vans and 11 buses with 305 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

7, 15

The senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senior class at High School A rented and filled 10 vans and 5 buses with 245 students. High School B rented and filled 2 vans and 7 buses with 259 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

13, 27

The senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senior class at High School A rented and filled 2 vans and 6 buses with 188 students. High School B rented and filled 12 vans and 6 buses with 318 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

11, 52

The senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senior class at High School A rented and filled 9 vans and 13 buses with 775 students. High School B rented and filled 14 vans and 13 buses with 830 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.

1, 1

The student council at Westford High School is raising money by selling hot apple cider and hot chocolate at this week's games. They sold 48 apple ciders and 13 hot chocolates at the football game, raising a total of $61. They raised $69 at the soccer game by selling 14 apple ciders and 55 hot chocolates. How much is the student council selling each drink for?

The sum of the digits of a certain two-digit number is 13. When you reverse its digits you increase the number by 9. Find the number.

The sum of the digits of a certain two-digit number is 17. When you reverse its digits you decrease the number by 9. What is the number?

The sum of the digits of a certain two-digit number is 4. Reversing its digits increases the number by 18. Find the number.

The sum of the digits of a certain two-digit number is 9. When you reverse its digits you decrease the number by 63. What is the number?

y - 8 = -0.2(x + 10)

The table represents a linear equation. Which equation shows how (-10, 8) can be used to write the equation of this line in point-slope form?

3, 4

To keep in shape, Beth exercises at a track near her home. She requires 18 minutes to do 2 laps running and 3 laps walking. In contrast, she requires 30 minutes to do 2 laps running and 6 laps walking. Assuming she maintains a consistent pace while running and while walking, how long does Beth take to complete a lap?

9, 6

Traveling downstream a certain boat went 15 km/h. Traveling upstream it only went 3 km/h. Find the speed of the boat in still water and the speed of the current.

5, 23

Tristan and Gordon, both teachers, are adding books to their class libraries. Tristan's classroom started out with a collection of only 13 books, but he plans to purchase an additional 2 books per week. Gordon's library started out with 8 books, and he has enough money in his budget to purchase another 3 books per week. At some point, the two teachers' libraries will contain the same number of books. How many weeks will that take? How many books will each class have?

2, 11

Two groups of volunteers are cleaning up the football stadium after the Homecoming game. Volunteers from the Band Booster Club have already cleaned 9 rows of bleachers and will continue to clean at a rate of 1 row per minute. The leadership class has completed 3 rows and will continue working at 4 rows per minute. Once the two groups get to the point where they have cleaned the same number of rows, they will take a break and decide how to split up the remaining work. How long will that take? How many minutes will each group have cleaned by then?

When you reverse the digits in a certain two-digit number you decrease its value by 18. Find the number if the sum of its digits is 12.

-2x+4y=-12

Which equation matches the line?

3x-4y=12

Which equation matches the line?

4x+3y=12

Which equation matches the line?

5x+2y=10

Which equation matches the line?

y = -1/2x + 5

Which equation represents the line that passes through (-6, 7) and (-3, 6)?

y = -5/8x + 6

Which equation represents the line that passes through (-8, 11) and (4, 7/2)?

13, 16

Willie and Scott are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and packages of gingerbread cookie dough. Willie sold 6 packages of white chocolate chip cookie dough and 3 packages of gingerbread cookie dough for a total of $126. Scott sold 7 packages of white chocolate chip cookie dough and 3 packages of gingerbread cookie dough for a total of $139. Find the cost each of one package of white chocolate chip cookie dough and one package of gingerbread cookie dough.

y = -3x