How do you come up with the equations?

Question

Kerry and Luke biked a total of 18 miles in one weekend. Kerry biked 4miles more than Luke. Write a system of equations and solve it to find how far each boy biked.

Answer 1

Let the number of miles biked by Kerry be X

 

Let the number of miles biked by Luke be Y

 

Since together they biked 18 miles, then, X + Y = 18   (1)

 

Kerry biked 4 miles more than Luke; then, X - Y = 4   (2)

 

from (2) X = 4 + Y

 

Substituting this in equation (1); (4 + Y) + Y = 18

 

4 + 2y = 18; 2Y = 18 - 4 = 14

 

2Y = 14, dividing through by 2 gives Y = 7

 

returning to (1); X = 18 - Y. ; X = 18 - 7 = 11

 

Hence Kerry biked 11 miles, and Luke biked 7 miles