Question

A cab company charges $3.10 flat rate in addition to $0.85 per mile. Rex has no more than $15 to spend on a ride. Write an inequality that represents Rex's situation. How many miles can Rex travel without exceeding his limit? Round off your answer to nearest tenth.

Answer 1

`3.10 + 0.85m \leq 15`

`m \leq 14.0`

Explanation:

Given

`Flat\ Rate = \$3.10`

`Addition = \$0.85` (per mile)

`Maximum\ Amount = \$15`

Required

Determine the inequality that represents the scenario and solve

Let the number of miles be represented by m.

The company's charges can be calculated using:

`Flat\ Rate + Additional\ Charges * m`

Substitute values

`\$3.10 + \$0.85 * m`

Rex can't exceed $15 implies that the company's charges can't exceed Rex's budget.

This is expressed as:

`\$3.10 + \$0.85 * m \leq \$15`

`\$3.10 + \$0.85m \leq \$15`

`3.10 + 0.85m \leq 15` ---- The inequality

Solving for m: Collect Like Terms

`0.85m \leq 15 - 3.10`

`0.85m \leq 11.9`

Divide through by 0.85

`m \leq 11.9/0.85`

`m \leq 14.0` ---- The solution

Answer 2

Explanation:

Let the total number of miles Rex can travel be x;

If a cab company charges $0.85 per mile, then x miles will cost $0.85x

If the flat rate rate charge is $3.10, the total price for x miles will be;

0.85x + 3.10

Since Rex has no more than $15 to spend on a ride, the inequality to represent the equation will be;

0.85x + 3.10 ≤ 15 (less than or equal to means that the total value cannot exceed $15)

Next is to solve for x

Given

0.85x + 3.10 ≤ 15

subtract 3.10 from both sides

0.85x + 3.10-3.10 ≤ 15-3.10

0.85x ≤ 15-3.10

0.85x ≤ 11.90

x ≤ 11.90/0.85

x ≤ 14

This means that Rex can travel 14 miles without exceeding his limit