9. Douglas bought a \( \$ 20 \) game card at a game center. The go-karts cost \( \$ 3.50 \) each time you race. He wants to have at least \( \$ 7.75 \) left on his card to play arcade games. Write and solve an inequality to determine how many times Douglas can race the go-karts. Then interpret the solution.

To determine how many times Douglas can race the go-karts while ensuring he has at least \$7.75 left, we set up the inequality based on his total budget. Let \( x \) be the number of times he races. The cost of racing \( x \) times is \( 3.50x \), and he must have at least \$7.75 remaining after the races. The initial amount on the card is \$20, so we can write the inequality: \[ 20 - 3.50x \geq 7.75 \] Now, let's solve the inequality: 1. Subtract 7.75 from both sides: \[ 20 - 7.75 \geq 3.50x \] 2. Calculate the left side: \[ 12.25 \geq 3.50x \] 3. Divide both sides by 3.50: \[ \frac{12.25}{3.50} \geq x \] 4. Calculate the division: \[ 3.5 \geq x \] This means \( x \leq 3.5 \). Since \( x \) must be a whole number (you can't race a fraction of a time), the maximum number of times Douglas can race is 3. Now, interpreting the solution: Douglas can race the go-karts 3 times and still have at least \$7.75 left on his game card, which means he can then enjoy playing arcade games afterward! If he races any more than that, he’ll be left with less than the minimum amount needed for arcade fun.