Question

Mrs. Freeman wants to get family portraits taken and is comparing prices between two different photography studios. Lin Photography charges $16 per portrait sheet, plus $10 for the session fee. Lasting Memories Company charges $60 for the session fee and $6 per portrait sheet. If Mrs. Freeman plans to purchase a certain number of portrait sheets, the cost will be the same at either studio. How many portrait sheets would that be?Write a system of equations, graph them, and type the solution.

Answer 1

Solution:

Let the number of portrait sheets be

$=x$

Step 1:

For lin photography, she is charged at $16 per portrait sheet

This can be represented below as

$16\times x=16x$

By adding the $10 session fee, the equation for Lin photography will be

$c(x)=16x+10\ldots\ldots\text{.}(1)$

Step 2:

For lasting memories company, she is charged $6 per portrait sheet

This can be represented below as

$6\times x=6x$

By adding the $60 session fee, the equation for lasting memories company will be

$c(x)=6x+60\ldots\ldots..\text{.}(2)$

Step 3:

Since the cost will be the same at either studio, then we will have to equate both equations together

$\text{eqn 1=eqn 2}$

By substituting the equations, we will have

$16x+10=6x+60$

Collect similar terms by substracting 6x from both sides and by substracting 10 from both sides

$\begin{gathered} 16x+10=6x+60 \\ 16x-6x+10-10=6x-6x+60-10 \\ 10x=50 \\ \text{divide both sides by 5} \\ \frac{10x}{10}=\frac{50}{10} \\ x=5 \end{gathered}$

Step 4:

Substitute the value x=5 in any of equations (1) or (2)

$\begin{gathered} c(x)=6x+60 \\ c(x)=6(5)+60 \\ c(x)=30+60 \\ c(x)=90 \\ \\ c(x)=16x+10 \\ c(x)=16(5)+10 \\ c(x)=80+10 \\ c(x)=90 \end{gathered}$

By graphing the equation, we will have the graph below

The point where the two lines meet is the solution of the linear equations which is at (5, 90)

Therefore,

The number of portrait sheets to be taken by two companies at the same price = 5

The prices each studio will charge = 90

The equation for Lin photography is C(x) =16x + 10

The equation for lasting memories company is C(x) =6x + 60

Hence,

we can say the solution can be written in a coordinate form as ( 5 , 90 )