The sum of two mystery numbers is 40. The bigger number is ten more than twice the smaller number. What are the two mystery numbers?

1 Answer
Mar 24, 2018

$10 \mathmr{and} 30$

Explanation:

Let the smaller number be $\boldsymbol{a}$ and the bigger number be $\boldsymbol{b}$

$b$ is 10 more than twice $a$:

$b = 2 a + 10$

The sum of these is 40:

$a + b = 40 \implies a + \left(2 a + 10\right) = 40$

Solving for $a$:

$a + \left(2 a + 10\right) = 40$

$3 a + 10 = 40$

$3 a = 40 - 10$

$3 a = 30$

$a = \frac{30}{3}$

$a = 10$

If $a = 10$ and $b = 2 a + 10$

Then:

$b = 2 \left(10\right) + 10 = 30$

The two numbers are:

$10 \mathmr{and} 30$