Question

Mrs. McCormick wants to get family portraits taken and is comparing prices between twodifferent photography studios. Dudley Photography charges $32 per portrait sheet, plus $46for the session fee. Lasting Memories Company charges $76 for the session fee and $17 perportrait sheet. If Mrs. McCormick plans to purchase a certain number of portrait sheets, thecost will be the same at either studio. What would the total cost be? How many portraitsheets would that be?

Answer 1

We have the following:

We have the following equations

Dudley Photography

`D=46+32x`

Lasting Memories Company

`L=76+17x`

Where x is the number of portrait sheet

Now, to calculate when the cost will be the same in any study, we must equalize the equations in the following way

D = L

replacing:

`46+32x=76+17x`

solving for x:

`\begin{gathered} 32x-17x=76-46 \\ 15x=30 \\ x=(30)/(15) \\ x=2 \end{gathered}`

Which means that at 2 portrait sheets the cost is the same.

Now, we calculate the cost:

`\begin{gathered} D=46+32\cdot2=110 \\ L=76+17\cdot2=110 \end{gathered}`

The cost is $110