Topic 4 Study Guide

Front

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.

Back

Total price = 2.19g + 0.59b + 1.49p

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.

Front

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. What is the total cost of 3 pounds of grapes, 3 pounds of bananas, and 2 pounds of pears?

Back

$11.32

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.

Front

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

Back

2x + 12

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.

Front

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?

Back

15x + 7

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.

Front

11.5 ounces of cereal in a container. Additional cereal is poured at 2.25 ounces per second for 4 seconds. Total ounces?

Back

20.5 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.

Front

Factor the expression 8a + 16c using the GCF.

Back

8(a + 2c)

Answer explanation

To factor 8a + 16c, find the GCF, which is 8. Factoring out 8 gives 8(a + 2c). This matches the correct choice, 8(a + 2c), as it simplifies the expression correctly.

Front

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

Back

−12b + 6c + 18

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.

Front

Combine like terms and factor the expression −4b + 8c + 12 − 8b − 2c + 6 using the GCF.

Back

6(-2b + c + 3)

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.

Front

Expression: −4b + 8c + 12 − 8b − 2c + 6. Evaluate for b = 2 and c = −3.

Back

-24

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.

Front

What is the total cost for 3 pounds of grapes at $2.19 per pound, 3 pounds of bananas at $0.59 per pound, and 2 pounds of pears at $1.49 per pound?

Back

$11.32

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.