10. Open Response Robin was given a \( \$ 40 \) monthly allowance. She wants to go to the movies as many times as possible and have at least \( \$ 12.50 \) left at the end of the month to go to a concert. A movie ticket costs \( \$ 5 \). Write and solve an inequality to determine how many times Robin can go to the movies this month. Then interpret the solution.

To determine how many times Robin can go to the movies, we can set up the inequality based on her monthly allowance and her minimum savings requirement. Let \( x \) be the number of movie tickets Robin buys. The cost of the movie tickets would be \( 5x \), and she wants to have at least \( 12.50 \) left over from her \( 40 \) dollar allowance. Therefore, we can write the inequality as follows: \[ 40 - 5x \geq 12.50 \] Now, let's solve the inequality: 1. Subtract \( 12.50 \) from both sides: \[ 40 - 12.50 \geq 5x \] \[ 27.50 \geq 5x \] 2. Next, divide both sides by \( 5 \): \[ \frac{27.50}{5} \geq x \] \[ 5.5 \geq x \] This means that \( x \leq 5.5 \). Since Robin can't go to the movies a fractional number of times, we round down to the nearest whole number, which means she can go to the movies a maximum of 5 times. Interpreting the solution, Robin can enjoy 5 movie outings this month while still ensuring she has enough money left over for her concert. This plan allows her social activities without sacrificing her other entertainment interests!