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.

Answer 1

The first step to solve the present question is to determine each of the equations to determine the number of each accessory as a function of the number of boxes, If d is the number of boxes, Nt is the number of Turbo Jet Pack, Nx is the number of X-Ray Vision Glasses, and Ni is the number of invisible shields, we have the following:

`\begin{gathered} N_T=6d+7 \\ N_X=2d-5 \\ N_I=10d+1 \end{gathered}`

Now, we can use it to solve the question.

Part A

It Nl is the number of Laser Sabers sold, let's transform the statement into a math equation, we have the following:

`N_L=1.5*(N_I-N_X)`

If we substitute the expressions we have from the previous-developed expressions, we have the following:

`\begin{gathered} N_L=1.5*(10d+1-(2d-5)) \\ N_L=1.5*(10d+1-2d+5) \\ N_L=1.5*(8d+6) \\ \\ N_L=12d+9 \end{gathered}`

Part B

Let's assume the value of a single Laser Saber is given by Vl, then the total value for the value of a unity times the number of sold Laser Sabers, as follows:

`\begin{gathered} T=V_L* N_L \\ T=V_L*(12d+9) \end{gathered}`