Question

There are two numbers whose sum is 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers?

Answer 1

18 and 35. The numbers whose sum 53 are 18 and 35.

The key to solve this problem is using a system of equations.

There are two numbers whose sum is 53. This number can be represented as x and y. So:

x + y = 53

Three times the smaller number is equal to 19 more than the larger. Let's set x as the smaller number and y the larger number. So:

3x = 19 + y

Clear y in both equations and let's use the equalization method to solve for x:

y = 53 - x and y = 3x - 19

Then,

53 - x = 3x - 19

53 + 19 = 3x + x ---------> 3x + x = 53 + 19 -------> 4x = 72

x = 72/4 = 18

To find y, let's substitute x = 18 in the equation x + y = 53

18 + y = 53 --------> y = 53 - 18

y = 35