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:

$\begin{gathered} 32x-17x=76-46 \\ 15x=30 \\ x=\frac{30}{15} \\ x=2 \end{gathered}$

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