Systems of Equations Word Problems

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?

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.

$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?

$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?

7, 11

Find the value of two numbers if their sum is 18 and their difference is 4.

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.

9, 6

Going down the river a boat went 15 km/h. Going up the river it only went 3 km/h. What is the speed of the current? How fast would the boat go if there were no current?

$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.

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?

$3, $10

Maria and Gabriella each improved their yards by planting hostas and ornamental grass. They bought their supplies from the same store. Maria spent $167 on 9 hostas and 14 bunches of ornamental grass. Gabriella spent $149 on 3 hostas and 14 bunches of ornamental grass. What is the cost of one hosta and the cost of one bunch of ornamental grass?

$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?

$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?

$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?

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.

$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, $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.

$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?

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?

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.

67

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.

13

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

81

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?

7, 10

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

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?