C. 16 solve lingar equations with variables on both sides: word problems H9G Jill wants to have a bowling party with her friends. Normally, the local bowling alley charges \( \$ 4 \) per person to bowl and \( \$ 3 \) per person for shoe rentals. However, the alley also has a group rate of \( \$ 90 \) for everyone to bowl, along with a discounted rate of \( \$ 2 \) per person for shoe rentals. How many people would need to go to the party for the two options to cost the same?

To find out how many people would need to go to the party for the two options to cost the same, we can set up an equation based on the costs of each option. **Option 1: Pay per person** - Cost to bowl: \( \$4 \) per person - Cost for shoe rentals: \( \$3 \) per person - Total cost for \( x \) people: \[ \text{Cost}_1 = 4x + 3x = 7x \] **Option 2: Group rate** - Group rate for bowling: \( \$90 \) - Discounted shoe rental: \( \$2 \) per person - Total cost for \( x \) people: \[ \text{Cost}_2 = 90 + 2x \] Now, we set the two costs equal to each other to find \( x \): \[ 7x = 90 + 2x \] Next, we solve for \( x \): 1. Subtract \( 2x \) from both sides: \[ 7x - 2x = 90 \] \[ 5x = 90 \] 2. Divide both sides by \( 5 \): \[ x = \frac{90}{5} = 18 \] Thus, **18 people** would need to go to the party for the two options to cost the same.