Question

david is driving his car on a business trip. he knows he will drive for at least 94 kilometers on the trip. also, he will drive for at most 115 kilometers on the trip (so that his company can cover his gas expenses). he has 3 days left on the trip. let x be the number of kilometers per day he will drive for those 3 days. he has already driven the car for 55 kilometers on the trip. (a) find the possible numbers of kilometers per day he will drive. write your answer as a compound inequality solved for x. (b) on the number line below, graph the solution that represents the possible numbers of kilometers per day he will drive.

Explanation:

Step1: Define total distance inequality

The total distance is already driven (55 km) plus 3 days of driving at \( x \) km/day. It must be at least 94 and at most 115. So, \( 55 + 3x \geq 94 \) and \( 55 + 3x \leq 115 \).

Step2: Solve \( 55 + 3x \geq 94 \)

Subtract 55: \( 3x \geq 94 - 55 = 39 \). Divide by 3: \( x \geq 13 \).

Step3: Solve \( 55 + 3x \leq 115 \)

Subtract 55: \( 3x \leq 115 - 55 = 60 \). Divide by 3: \( x \leq 20 \).

Step4: Combine inequalities

The compound inequality is \( 13 \leq x \leq 20 \).

Answer:

\( 13 \leq x \leq 20 \)