# How do you find two numbers which differ by 5, such that twice the first number less three times the second will give an answer of 2?

Mar 16, 2017

The second number is $8$ and the first number is $13$

#### Explanation:

Write an expression for each of the numbers in terms of $x$ and then make an equation.

Let the second number be $x$.
The first number is $x + 5$

Twice the first, less three times the second $= 2$

$2 \left(x + 5\right) - 3 \left(x\right) = 2$

$2 x + 10 - 3 x = 2$

$10 - 2 = 3 x - 2 x \text{ } \leftarrow$ to keep the values positive.

$8 = x$

The second number is $8$ and the first number is $13$

Check:

$2 \times 13 - 3 \times 8 = 26 - 24 = 2$
Checks out fine!