Topic 4 Study Guide

The price of grapes is $2.19 per pound. The price of bananas is $0.59 per pound. The price of pears is $1.49 per pound. Write an expression to represent the total price of g pounds of grapes, b pounds of bananas, and p pounds of pears.

• Total price = 2.19g + 0.59b + 1.49p

• Total price = 1.99g + 0.49b + 1.29p

• Total price = 2.29g + 0.69b + 1.59p

• Total price = 2.09g + 0.79b + 1.39p

Answer explanation

The total price is calculated by multiplying the price per pound of each fruit by the number of pounds. Thus, the correct expression is 2.19g + 0.59b + 1.49p, which matches the first answer choice.

The price of grapes is $2.19 per pound. The price of banas is $0.59 per pound. The price of pears is $1.49 per pound. What is the total cost of 3 pounds of grapes, 3 pounds of bananas, and 2 pounds of pears?

• The total cost for 3 pounds of grapes, 3 pounds of bananas, and 2 pounds of pears is $10.53.

• The total cost for 3 pounds of grapes, 3 pounds of bananas, and 2 pounds of pears is $8.75.

• The total cost for 3 pounds of grapes, 3 pounds of bananas, and 2 pounds of pears is $11.32.

• The total cost for 3 pounds of grapes, 3 pounds of bananas, and 2 pounds of pears is $9.50.

Answer explanation

To find the total cost, calculate: 3 lbs of grapes at $2.19 = $6.57, 3 lbs of bananas at $0.59 = $1.77, and 2 lbs of pears at $1.49 = $2.98. Adding these gives $6.57 + $1.77 + $2.98 = $11.32, which is the correct answer.

On Saturday, Lukas drove 4x – 5 miles. On Sunday, he drove 3x – 10 miles. What is the difference in miles driven?

• x + 15

• x – 5

• x + 5

• x – 15

Answer explanation

To find the difference in miles driven, subtract the distance driven on Sunday from Saturday: (4x - 5) - (3x - 10) = x + 5. The correct answer is x + 5.

Simplify the expression 2(10) + 2(x – 4).

• A. 2x + 16

• B. x + 12

• C. 2x + 12

• D. x + 16

Answer explanation

To simplify 2(10) + 2(x – 4), first calculate 2(10) = 20. Then distribute 2 to (x – 4) to get 2x - 8. Combine like terms: 20 - 8 + 2x = 2x + 12. Thus, the correct answer is C. 2x + 12.

Suppose 8x + 16 ice cream cones were sold on Saturday and 7x – 9 were sold on Sunday. What is the total number of ice cream cones sold?

• 15x + 25

• 15x + 7

• x + 7

• x + 25

Answer explanation

To find the total ice cream cones sold, add the expressions: (8x + 16) + (7x - 9). This simplifies to 15x + 7. Thus, the correct answer is 15x + 7.

There are 11.5 ounces of cereal in a container. Additional cereal is poured into the container at a rate of 2.25 ounces per second. How many ounces are in the container after 4 seconds?

• 11.5 + (2.25 * 4) = 11.5 + 9 = 20.5 ounces

• 11.5 + (2.25 * 4) = 11.5 + 8 = 19.5 ounces

• 11.5 + (2.25 * 4) = 11.5 + 10 = 21.5 ounces

• 11.5 + (2.25 * 4) = 11.5 + 7 = 18.5 ounces

Answer explanation

To find the total ounces in the container after 4 seconds, calculate the additional cereal: 2.25 ounces/second * 4 seconds = 9 ounces. Then add this to the initial amount: 11.5 + 9 = 20.5 ounces, which matches the correct choice.

Select all correct ways of factoring −3x − 9.

• −3(x + 3)

• 3(x + 3)

• 3(−x − 3)

• −3(x − 3)

• 3(x − 3)

Answer explanation

To factor −3x − 9, we can factor out −3, giving us −3(x + 3). Alternatively, factoring out 3 gives us 3(−x − 3). Both are correct, while the other options do not correctly represent the original expression.

Consider the expression −4b + 8c + 12 − 8b − 2c + 6. Simplify the expression.

• −12b + 6c + 18

• −12b + 10c + 18

• −12b + 6c + 6

• −12b + 10c + 6

Answer explanation

Combine like terms: -4b - 8b = -12b, 8c - 2c = 6c, and 12 + 6 = 18. Thus, the simplified expression is -12b + 6c + 18, which matches the correct choice.

Consider the expression −4b + 8c + 12 − 8b − 2c + 6. Combine the like terms and then Factor the simplified expression using the GCF.

• −4(3b − 2c − 4)

• 6(-2b + c + 3)

• −2(6b + 3c + 9)

• −2(6b − 3c + 9)

Answer explanation

Combining like terms gives us: -12b + 6c + 18. Factoring out the GCF of 6 results in 6(-2b + c + 3), which matches the correct answer choice.

Consider the expression −4b + 8c + 12 − 8b − 2c + 6. What is the value of the expression when

b = 2 and c = −3?

• -24

• -20

• -10

• 0

Answer explanation

Substituting b = 2 and c = -3 into the expression gives: -4(2) + 8(-3) + 12 - 8(2) - 2(-3) + 6 = -8 - 24 + 12 - 16 + 6 + 6 = -24. Thus, the value of the expression is -24.