Question

The sum of two numbers is 90. The larger

number is 14 more than 3 times the smaller
number. Find the numbers.

Answer 1

`19\text{ and }71`

Explanation:

Let the smaller number be
`x`. The larger number can be represented by
`3x+14`

Solving, we get:

`x+3x+14=90,\\4x+14=90,\\4x=76,\\x=\boxed{19}`

The larger number is therefore
`90-19=\boxed{71}`

Answer 2

The numbers are 19 and 71.

Explanation:

Let x and y represent the two numbers. Then x + y = 90.

Also, if we assume that the larger number is y, then y = 3x + 14.

We must solve this system of linear equations. Since we already have the result of solution for y (y = 3x + 14), let's use the substitution method to find the solution:

x + y = 90 becomes x + 3x + 14 = 90, or:

4x = 76. Thus, x = 76/4, or 19. If x = 19, then y = 3(19) + 14, or y = 71.

The numbers are 19 and 71.

Note that these add up to 90, as they must, and that 71 is 14 more than 3 times 19.