Question

A toy store sells accessories to go with the latest action figure. The store projects that it will sell a certain number of accessories for every box of a dozen action figures it orders. Let d represent one box of a dozen action figures. A new accessory, the Laser Saber, has sales equal to 1.5 times the difference of the number of Invisible Shields and X-Ray Vision Glasses.Part AWrite an expression to represent the number of Laser Sabers sold.Part BHow would you write an equivalent expression for the price in simplified form? Explain.Part CAdd the expressions to find the total number of all four accessories sold.Part DIf the toy store sold 78 of the latest action figure, how many accessories did it sell? Explain.

Answer 1

a) 12d + 9

c) 30d + 12

d) 207

Step-by-step explanation:

First, we need to write an expression for each accessory.

Since d is the number of boxes, we get:

Turbo Jet Pack. Six times the number of boxes plus seven

6d + 7

X-Ray Vision Glasses. Five less than two times the number of boxes

2d - 5

Invisible Shield. One more than ten times the number of boxes

10d + 1

Part A.

Then, the Laser Saber has sales equal to 1.5 times the difference of the number of Invisible Shields and X-Ray Vision Glasses.

1.5((10d + 1) - (2d - 5))

Because 10d + 1 is the number of invisible shields and 2d - 5 is the number of X-Ray Vision Glasses.

Now, we can simplify the expression as

1.5(10d + 1 - 2d + 5)

1.5(8d + 6)

1.5(8d) + 1.5(6)

12d + 9

Part C.

Then, we need to add all the expressions before to get:

(6d + 7) + (2d - 5) + (10d + 1) + (12d + 9)

(6d + 2d + 10d + 12d) + (7 - 5 + 1 + 9)

30d + 12

Therefore, the total number of all four accessories is 30d + 12

Part D.

To know how many accessories did it sell, first, we need to find how many dozens are 78 action figures, so

78/12 = 6.5

Therefore, they sold 6.5 boxes of the action figure. Now we can find the number of accessories sold, replacing d with 6.5 in the expression of part C, so

30d + 12

30(6.5) + 12

195 + 12

207

Then, they sold 207 accessories.