Algebra 2.06: Applications of Linear Equations + quiz answers

Raisins sell for $3.50 per pound, and granola sells for $5.90 per pound. Terri bought some raisins and some granola. The total weight was 2.1 pounds and cost $8.79. How many pounds of raisins and how many pounds of granola did Terri buy?

1.5 pounds of raisins; 0.6 pounds of granola

The value of the nickels plus the value of the dimes is $9.25, represented by the equation 0.05n+0.10(2n)=9.25. Solve the equation.

2 times 37 is 74, so Ava has 37 nickels and 74 dimes

A rectangle has a length of 8.3 cm and a perimeter of 22.4 cm. Enter the width of the rectangle, in decimal form, in the box.

2.9 cm

Samuel paid $9.10, including tax, for a dog collar. Before tax, the original price of the collar was $8.75. What was the sales tax rate? Let r represent the rate as a decimal. Complete the equation that represents the problem. (Hint: The original price of the collar plus the amount of tax equals the total cost including tax.) Enter your response in the box.

8.75 + 8.75r - = 9.10

Formulas for volume

Cube: s3 or s cubed Prism: Bh (area of the base times height)

At noon, Jessica and her family left Grandma's house to drive north to their home. They reached their house at 1:30 p.m. Also leaving at noon, her cousin Jancy drove her family south from Grandma's house to their home. They arrived at 3 p.m. The driving distance from Jessica's house to Jancy's house is 288 mi and they both drove at the same speed. What was the speed?

Jessica and Jancy both drove at a rate, or speed, of 64 mph.

Logan has $2.55 worth of dimes and quarters in his pocket. The number of dimes is 3 more than twice the number of quarters. How many of each coin does he have?

Logan has 5 quarters and 13 dimes.

Mrs. Rivera went to the store to buy ingredients for trail mix. The store sells small bags of mixed nuts for $1.49 and small bags of dried fruit for $0.99. Her receipt shows she bought 17 bags for a total of $22.83. How many bags of mixed nuts and how many bags of dried fruit did Mrs. Rivera buy?

Mrs. Rivera bought 12 bags of mixed nuts and 5 bags of dried fruit.

Formulas for area

Square: s2 squared Rectangle: lw Triangle: 1/2bh or 1 half b h Circle: πr2 or pi r squared

How long is the biking portion?

The biking portion of the race is 11Km long.

At noon, Doug drove west from a gas station to a motel. He reached the motel at 3 p.m. Also leaving at noon, Ashley drove east from the same gas station to her sister's house. She arrived at 2:30 p.m. The driving distance from the motel to Ashley's sister's house is 341 mi. Ashley and Doug both drove at about the same speed, r.

The distance Doug drove to the motel can be represented by 3r The distance Ashley drove to her sister's house can be represented by 2.5r

A floor rug is rectangular in shape. The width of the rug is 4 ft less than its length. The perimeter of the rug is 40 ft. What are the rug's dimensions?

The length is 12 ft and the width is 8 ft.

Gina paid $39.59 for a new pair of shoes. The cost included a 7% sales tax. What was the cost of the shoes before the tax was applied?

The original price of the shoes was $37.

Solve the equation 8.75+8.75r=9.10. What is the sales tax rate?

The rate is 4%

Juan tutors students in math, chemistry, and Spanish. Last week he tutored 13 h total. He tutored 3 times as many hours of chemistry as math, and 1 more than twice as many hours of Spanish as math. How many hours of chemistry did he tutor?

The sum of the math and chemistry hours is 8. The number of hours tutoring Spanish is 1 more than twice the math hours, so the Spanish hours are 5. The sum of 8 and 5 is 13. The answer is correct.

Juan chooses 4 items for his main course, 1 drink, and 1 dessert in a restaurant. The total cost of the meal is $9.80. Each main course item costs $1.10 and the dessert costs 50¢ more than the drink. Let d represent Juan's dessert and r represent his drink.

The total amount Juan spent on his main course items can be found by multiplying:4×1.10 [true] An equation that models how much Juan spent on his drink and dessert is: 4.40 = d + r [false] A model for defining the cost of Juan's dessert in terms of his drink is: d = r − 0.50 [false] Juan spent $2.45 on his drink. [true] Juan spent $2.95 on his dessert. [true]

The sum of three consecutive even integers is 72. Let x represent the least consecutive integer. What equation could be used to find the least consecutive integer? What is the second consecutive integer? Enter your answers in the boxes.

x+x+2+x+4=72 24

The sum of the individual distances equals the length of the entire race, 23 km, so the equation is x+x+3+x/2=23. What is the value of x? Enter your response in the box.

x=8

A restaurant stocked up on pancake mix to accommodate its breakfast customers. Buckwheat mix costs $2.30/lb and whole wheat mix costs $1.85/lb. The restaurant bought a total of 23 lb of mix for $46.60. Let b represent the amount in pounds of buckwheat mix and w represent the amount in pounds of whole wheat mix. Select true or false for each statement.

An equation that can be used to define the amount of whole wheat mix in terms of the amount of buckwheat mix is w = 23 − b. [true] An equation that can be used to find the amount of buckwheat mix is 1.85b +2.30(23−b)=46.60. [false] A simplified equation that can be used to find the amount of buckwheat mix is 0.45b=4.05. [true] The restaurant bought 9 lb of buckwheat flour. [true] The restaurant bought 32 lb of whole wheat flour. [false]

The perimeter, P, of any rectangle is given by the formula P = 2l + 2w, where l represents the length of the rectangle and w represents the width. Let the length of a rectangle equal 3 more than 3 times its width, and the perimeter equal 54 ft.

An equation that can be used to define the length in terms of the width is: l=3(w+3) [False] An equation that can be used to find the perimeter in terms of the width is: 54 = 2(3w + 3) + 2w [True] A simplified equation that can be used to model this problem is: 54 = 8w [False] The width of the rectangle is 6 ft. [True] The length of the rectangle is 21 ft. [True]

Maddie's piggy bank contains $2.02 in dimes, nickels, and pennies. She has 3 more nickels than dimes and 5 fewer pennies than dimes. Let d represent the number of dimes in Maddie's piggy bank, p represent the number of pennies, and n represent the number of nickels. Select true or false for each statement.

An equation that can be used to define the number of nickels in terms of the number of dimes is n=d−3. [false] An equation that can be used to define the number of pennies in terms of the number of dimes is p=d+5. [false] An equation that can be used to find the number of dimes in Maddie's piggy bank is 0.10d+0.05(d+3)+0.01(d−5)=2.02. [true] Maddie had 12 dimes, 15 nickels, and 7 pennies. [true]

Substitute w and w + 6 into the formula for the perimeter of a rectangle. Simplify the right side. What equation do you get?

68=4w+12

Formulas for perimeter

square: 4s Rectangle: 2l + 2w Other polygons: sum of the side lengths Circle (circumference): 2πr

At what speed did Doug and Ashley both drive? Enter your response in the box.

62 mph

Ansley's age is 5 years younger than 3 times her cousin's age. Ansley is 31 years old. Let c represent Ansley's cousin's age. What expression, using c, represents Ansley's age? Enter your response in the box.

3c−5

You have two expressions for Ansley's age. Join them to form the equation 3c−5=31. Solve for c. Enter your response in the box

3c−5=31 3c−5+5=31+5 3c=36 3c/3=36/3 c=12

Enter an equation that can be used to solve this problem, where x represents the number of hours that the first plane had been traveling. Two planes left the same airport traveling in opposite directions. The first plane left the airport at 2 P.M. traveling at an average rate of 500 mph. The second plane left the airport at 4 P.M. traveling at an average rate of 550 mph. When will the planes be 3100 miles apart? Enter the amount hours, after the first plane left, when the planes will be 3100 miles apart.

500x+550(x−2)=3100 4

The perimeter, P, of any rectangle is given by the formula P=2l+2w , where l represents the length of the rectangle and w represents the width. George is drawing a rectangular plan for a playhouse he is building for his little sister. For the measurement of the width, he doubled the length and then subtracted 12 in. The perimeter of George's rectangular plan is 36 in. Select true or false for each statement.

An equation that can be used to define the width in terms of the length is: w = 2l−12 [true] An equation that can be used to find the perimeter in terms of the length is: 36 = 2l − 12 + 2l [false] A simplified equation that can be used to model this problem is: 12 = 6l [false] The width of the rectangle is 8 in. [true] The length of the rectangle is 10 in. [true]

Mrs. Fuller is building a deck. The composite deck material costs $9.20 per foot and the railing costs $6.40 per foot. Mrs. Fuller paid $1998 for 240 ft of materials, in total. Let d equal the length in feet of composite deck materials Mrs. Fuller bought and r equal the length in feet of railing materials. Select true or false for each statement.

An equation that can be used to model this problem is: 9.2d + 6.4r = 1998 [True] An equation that can be used to define the length of railing materials in terms of the length of deck materials is: r = 240 − d [True] After substitution, the model for this problem becomes: 9.2d + 6.4(240 − d) = 1998 [True] Mrs. Fuller bought 165 ft of railing materials. [false] Mrs. Fuller bought 75 ft of composite deck materials. [false]

Merv has two jobs. He earns a salary of $45,000 per year as an accountant and $10.50 per hour at his part-time job. Merv earned $48,570 last year. Let h represent the number of hours Merv worked at his part-time job. Select true or false for each statement.

The total amount Merv made working at his part-time job can be found by dividing: 48,570 ÷ 10.50 [false] The total amount Merv made working at his part-time job can be found by subtracting: 48,570 − 45,000 [true] An equation that models how many hours Merv worked at his part-time job is: 3570 = 10.50h [true] An equation that models how many hours Merv worked at his part-time job is: 48,570 = 10.50h [false] Merv worked about 4626 hours at his part-time job. [false] Merv worked exactly 340 hours at his part-time job.[true]

Ghamba is wallpapering a room in her house. Regular wallpaper rolls cost $12.99 per roll and border rolls cost $5.99 per roll. Ghamba bought 12 rolls and paid $134.88. How many rolls of each type did she buy? Let r represent the number of regular rolls Ghamba bought and b represent the number of border rolls. Select true or false for each statement.

The total number of border rolls Ghamba bought can be modeled with the equation: b=12−r [true] The total number of regular rolls Ghamba bought can be found by solving the equation: 12.99r + 5.99(12 − r) = 134.88 [true] Ghamba bought 3 rolls of regular wallpaper. [false] Ghamba bought 9 rolls of border wallpaper. [false]

The length of a rectangle is 6 ft more than its width. The perimeter of the rectangle is 68 ft. What are the dimensions of the rectangle?

The width is 14ft and the length is 20ft.

Distance formula

d = rt

A race consists of three parts: a long run, biking, and a short run. The biking portion is 3 km longer than the long run and the short run is half the distance of the long run. The entire race is 23 km long. How long is the biking portion? Drag and drop the expression with the matching word phrase.

long run x biking x+3 short run x/2

Mindy is 3 years older than two times her brother Jake's age. Let j represent Jake's age and m represent Mindy's age. Which equation represents Mindy's age?

m = 2j + 3

Ava's piggy bank contains only nickels and dimes, with a total value of $9.25. The number of dimes is twice the number of nickels. How many of each coin does she have? Let n equal the number of nickels.

number of nickels n number of dimes 2n value of nickels 0.05n value of dimes 0.10(2n)