Equivalent Expressions from Situations

The perimeter of square F is  $\frac{2}{3}$  meter less than the perimeter of square G. The side lengths of square F are each f meters, and the side lengths of square G are each  $\frac{1}{4}\left(f-\frac{2}{3}\right)$ meters. Which expression also represents the side lengths of square G?

• $\frac{1}{4}f-\frac{1}{6}$

• $\frac{1}{4}f-\frac{2}{3}$

• $\frac{1}{4}f-\frac{3}{7}$

• $\frac{1}{4}f-\frac{11}{12}$

The bottles of juice that Craig usually buys each have x ounces of juice in them. Another company makes bigger bottles of juice that each have 10% more juice in them than the bottles that Craig usually buys. Craig buys 8 bottles of the bigger size. The total amount of juice, in ounces, he buys is represented by the expression shown below.

 $8(x+0.1x)$  

Which expression also represents the total amount of juice, in ounces, Craig buys?

• $0.8x$
  

• $1.8x$
  

• $8.1x$
  

• $8.8x$

Pencils come in two different-sized packages. Each of the smaller packages contains p pencils. The larger packages each contain p + 4 pencils. Jake bought some of the smaller packages, some of the larger packages, and 8 extra pencils as well. To represent the total number of pencils he bought, Jake wrote 4p + 2(p + 4) + 8.

Which expression is equal to the number of pencils Jake bought?

• 5p + 14

• 5p + 16

• 6p + 12

• 6p + 16

At a carnival, Andrew went on rides and played games. 

• Each ride cost $2. 

• Each game cost $2. 

• Andrew went on 3 rides and played g games. 

Andrew wrote the expression below to represent the total amount of money, in dollars, he spent at the carnival.

 $6+2g$  

 Which of the following is another way Andrew could represent the total amount of money, in dollars, that he spent at the carnival?

•  $2\times3g$  

•  $2\left(3+g\right)$  

•  $4\times3g$  

•  $4\left(3+g\right)$  

Which TWO expression(s) can be used to find the perimeter. (Select two answers!)

• x + x + x + 5+ x + 5

• 4x + 10

• 4+ x + 5

• 14x

Write a simplified expression to represent the perimeter of the shape.

• 20x - 8

• 10x - 4

• 25x - 4

• 5x + 5x - 4

Which algebraic expression represents the area of the given rectangle>

• 4x+5

• 4x+20

• 20x

• 2x+18

What expression represents the area of this shape?

• 6x + 18y + 12

• 6x + 3y + 2

• 6x + 18y + 2

• none of those

 $3.5x+4.8?$  

Which expression is equivalent to

•  $3\cdot0.5x+4\cdot0.8$  

•  $3x\cdot0.5x+4\cdot0.8$  

•  $3\cdot0.5x+4+0.8$  

•  $3x+0.5x+4+0.8$  

Kathy purchased cereal in bulk on two different trips to a grocery store. She paid $5.79 per pound each

time. She purchased 2.25 pounds the first time and 1.8 pounds the second time.

Rounded to the nearest cent, what is the total amount Kathy paid for both cereal purchases?

• $9.84

• $12.67

• $14.83

• $23.45