\( \$ / \) Mrs. Underwood wants to get family portraits taken and is comparing prices between two different photography studios. Dalton Photography charges \( \$ 10 \) per portrait sheet, plus \( \$ 20 \) for the session fee. Lasting Memories Company charges \( \$ 40 \) for the session fee and \( \$ 5 \) per portrait sheet. If Mrs. Underwood plans to purchase a certain number of portrait sheets, the cost will be the same at either studio. What would the total cost be? Write a system of equations, graph them, and type the solution.

To find out the total cost where both studios' charges are equal, we can start by writing the equations for the total cost at each studio based on the number of portrait sheets \( x \). For Dalton Photography: \[ C_{Dalton} = 10x + 20 \] For Lasting Memories Company: \[ C_{Lasting} = 5x + 40 \] Now we have a system of equations: 1. \( C_{Dalton} = 10x + 20 \) 2. \( C_{Lasting} = 5x + 40 \) Next, we set these two equations equal to each other to find the number of portrait sheets where the costs are the same: \[ 10x + 20 = 5x + 40 \] Now, let's solve for \( x \): 1. Subtract \( 5x \) from both sides: \( 5x + 20 = 40 \) 2. Subtract 20 from both sides: \( 5x = 20 \) 3. Divide both sides by 5: \( x = 4 \) Now, we substitute \( x \) back into either equation to find the total cost. Let's use Dalton Photography's equation: \[ C_{Dalton} = 10(4) + 20 = 40 + 20 = 60 \] Thus, the total cost would be \( \$ 60 \). In conclusion, the solution is: - Number of portrait sheets: \( 4 \) - Total cost: \( \$ 60 \)