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

The larger number is 71 and the smaller number is 19.

Two equations can be derived from the question:

x + y = 90 equation 1

x = 14 + 3y equation 2

The larger number would be represented with x and the smaller number would be represented with y.

Substitute for x in equation 1

14 + 3y + y = 90

Add similar terms

14 + 4y = 90

Make y the subject of the formula

4y = 90 - 14

4y = 76

y = 76 / 4 = 19

Substitute for y in equation 1

x + 19 = 90

x = 90 - 19

x = 71

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Answer 2

The sum of numbers is the addition of the numbers.

The numbers are 19 and 71

Let the two numbers be x and y, where y is greater than x.

So, we have:

$\mathbf{y = 3x + 14}$

The sum of the numbers is:

$\mathbf{x +y = 90}$

Substitute $\mathbf{y = 3x + 14}$

$\mathbf{x +3x + 14 = 90}$

$\mathbf{4x + 14 = 90}$

Subtract 14 from both sides

$\mathbf{4x = 76}$

Divide both sides by 4

$\mathbf{x = 19}$

Substitute $\mathbf{x = 19}$ in $\mathbf{y = 3x + 14}$

$\mathbf{y = 3(19) + 14}$

$\mathbf{y = 71}$

Hence, the numbers are 19 and 71

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