Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Mrs. Bennett wants to get family portraits taken and is comparing price... Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Mrs. Bennett wants to get family portraits taken and is comparing prices between two different photography studios. Farrell Photography charges $27 per portrait sheet, plus $74 for the session fee. Lasting Memories Company charges $82 for the session fee and $25 per portrait sheet. If Mrs. Bennett 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? What would the total cost be? If Mrs. Bennett orders ___ portrait sheets, the portrait session will cost $___ at either studio. Read more

Steps to Solve

1. Set up the equations for each studio's pricing

Let ( x ) be the number of portrait sheets Mrs. Bennett orders.

For Farrell Photography, the total cost ( C_1 ) can be expressed as: $$ C_1 = 27x + 74 $$

For Lasting Memories Company, the total cost ( C_2 ) can be expressed as: $$ C_2 = 25x + 82 $$

2. Set the equations equal to each other

Since we want the costs to be the same at either studio, we set the two equations equal: $$ 27x + 74 = 25x + 82 $$

3. Solve for ( x )

First, we will isolate ( x ) by subtracting ( 25x ) from both sides: $$ 27x - 25x + 74 = 82 $$

This simplifies to: $$ 2x + 74 = 82 $$

Next, subtract ( 74 ) from both sides: $$ 2x = 8 $$

Then divide by ( 2 ) to find ( x ): $$ x = 4 $$

4. Calculate the total cost

Now that we have ( x ), we can find the total cost using either studio's equation. Using Farrell Photography's equation: $$ C_1 = 27(4) + 74 = 108 + 74 = 182 $$

So, the total cost is $182.