Question

Gavin went on 25 runs last month that totaled 101 miles. Each run was a distance of either 3 miles or 5 miles. Which system of equations can be used to determine the number of 3-mile runs, x, and the number of 5-mile runs, y, that Gavin went on last month?

Answer 1

Hence, the number of 3-miles run Gavin went on last month=12.

and number of 5-miles run Gavin went on last month=13.

Explanation:

'x' denotes the number of 3-miles run.

'y' denotes the number of 5-miles run.

Gavin went on 25 runs.

that means x+y=25-------(1).

also he total walked 101 miles that means in equation it could be written as:

3x+5y=101--------(2)

on solving equation (1) and (2) by method of elimination.

multiply equation (1) by 3 and subtract from equation (2) we get:

equation (1) transformed to 3x+3y=75

3x+5y=101

3x+3y=75

- - -

---------------

2y=26

⇒ y=13.

and putting value of y in equation (1) we get:

x=12.

Hence, the number of 3-miles run Gavin went on last month=12.

and number of 5-miles run Gavin went on last month=13.