Practice Topic 4 Assessment

The price of grapes, g, is $3.19 per pound. The price of bananas, b, is $0.69 per pound. The price of pears, p, is $1.69 per pound. First, write an expression to represent the total price of the fruit. Then, calculate the total cost for 4 pounds of grapes, 4 pounds of bananas, and 3 pounds of pears? Your answer should be in the following format: The expressions is ______: The total cost is ______.

(a)  

Answer explanation

3.19g + 0.69b + 1.69p

substitute:

3.19(4) + 0.69(4) + 1.69(3)

multiply and add

12.76 + 2.76 + 5.07

20.59

On Saturday, Lukas drove 6x – 5 miles. On Sunday, he drove 5x – 10 miles. What is the difference in miles driven?

• x + 15
• x – 5
• x + 5
• x – 15

Answer explanation

On Saturday, Lukas drove 6x – 5 miles. On Sunday, he drove 5x – 10 miles. What is the difference in miles driven?

Difference is the key word that indicates subtraction:

(6x - 5) - (5x - 10) = 6x -5 - 5x + 10

6x - 5x = 1x or x

-5 + 10 = 5

x + 5

• –30 + 40d – 10c
• –6 + 8d – 2c
• –2c + 8d – 6
• 6 – 8d + 2c

Simplify this expression. 2(20) + 2(x – 6)

• 2x + 34
• x + 28
• 2x + 28
• x + 34

Answer explanation

2(20) + 2(x – 6)

2 * 20 = 40

2 * x = 2x

2 * -6 = -12

40 + 2x - 12

40 - 12 = 28

2x + 28

A store offers 30% off all items. If x is the original purchase price, which expression represents the final price with the discount? Select all that apply.

• 1.3x
• 0.7x
• x
• x – 0.3x
• x + 0.3x

Answer explanation

A store offers 30% off all items. If x is the original purchase price, which expression represents the final price with the discount?

100% - 30% = 70% which as a decimal is 0.7. If you multiply 0.7 by x you get 0.7x.

You could also find the discount amount (0.3x) and subtract it from the original price (x)

x - 0.3x

Suppose 9x + 18 ice cream cones were sold on Saturday and 8x – 12 were sold on Sunday. What is the total number of ice cream cones sold?

• 17x + 30
• 17x + 6
• x + 6
• x + 30

Answer explanation

Suppose 9x + 18 ice cream cones were sold on Saturday and 8x – 12 were sold on Sunday. What is the total number of ice cream cones sold?

We have an addition problem which means we simply need to combine like terms.

9x +8x = 17x

18 - 12 = 6

17x + 6

There are 10.5 ounces of cereal in a container. Additional cereal is poured into the container at a rate of 3.25 ounces per second. How many ounces are in the container after 6 seconds?

Mathematical Equivalence

ON

Answer explanation

There are 10.5 ounces of cereal in a container. Additional cereal is poured into the container at a rate of 3.25 ounces per second. How many ounces are in the container after 6 seconds?

Start: 10.5

add: 3.25 oz per second for 6 seconds

10.5 + (3.25 * 6) = 10.5 +19.5 = 30

What are two different ways of factoring –2x – 4? Select all that apply.

• –2(x + 2)
• 2(x + 2)
• 2(–x – 2)
• –2(x – 2)

Answer explanation

two different ways of factoring –2x – 4

Positive and negative factors

2(-x -2)

-2(x + 2)

• -1/5x + 1/4
• - x + 1/4
• -3/4x + 1/5

Use the expression 8a + 24c. Factor the expression using the GCF.

• 2(4a + 12c)
• 4(2a + 6c)
• 8(a + 3c)
• 16(1/2a + c)

Answer explanation

8a + 24c: factor using the GCF

8 goes into 8 AND 24 so it is the GCF

8a ÷ 8 = 1a or a

24c ÷ 8 = 3

8(a + 3c)