Question

The larger of two numbers is 15 more than the smaller number. If the sum of the two numbers is 27, find the two numbers.

Larger Number:
Smaller Number:

Answer 1

Larger number: 21

Smaller number: 6

Explanation:

Step 1: Make equations.

x ... larger number

y ... smaller number

First equation: The larger of two numbers is 15 more than the smaller number.

x = y + 15

Second equation: Sum of the two numbers is 27.

x + y = 27

Step 2: Solve the system of equations.

First equation: x = y + 15

Second equation: x + y = 27

Substitute x in second equation with x from first.

x + y = 27

(y + 15) + y = 27

Solve for y.

y + 15 + y = 27

2y = 27 - 15

2y = 12

y = 6

Substitute the calculated value of y back in first equation to get x.

x = y + 15

x = 6 + 15

x = 21