Question

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 an inequality to determine how many times douglas can race the go - karts.
20 - 3.5x ≥ 7.75
correct answer
20 - 3.5x ≥ 7.75
part b
incorrect
1 try left. try once more
the solution of the inequality in part a is x ≤ 3.5. this means that douglas can race the go - karts no more than 3 times.

Explanation:

Step1: Solve the inequality \(20 - 3.5x \geq 7.75\)

Subtract 20 from both sides: \(-3.5x \geq 7.75 - 20\)
\(-3.5x \geq -12.25\)

Step2: Divide both sides by -3.5 (remember to reverse the inequality sign)

\(x \leq \frac{-12.25}{-3.5}\)
\(x \leq 3.5\)

Since \(x\) represents the number of times Douglas can race the go - karts, and the number of races must be a non - negative integer, the maximum number of times he can race is 3 (because 3.5 is not an integer and he can't race half a time, so he can race no more than 3 times).

Answer:

The solution of the inequality \(20 - 3.5x \geq 7.75\) is \(x\leq3.5\), and Douglas can race the go - karts no more than 3 times.