Solving a word problem involving a sum and another basic relationship using a system of linear equations

Question

The sum of two numbers is 53

. The larger number is 15

 more than the smaller number. What are the numbers?

Answer 1

let the larger number be X. Let the smaller number be Y.

X + Y =53

X - Y =15

Adding the above two equations together,

X +Y+X-Y =53+15

2X =68

X =34

X+Y =53

34 + Y = 53

Y = 53-34

Y = 19

The end.