# The sum of two numbers is twice their difference. The larger number is 6 more than twice the smaller. How do you find the numbers?

a = 18
b = 6

#### Explanation:

a = larger number
b = smaller number

$a + b = 2 \left(a - b\right)$
$a = 2 b + 6$

$a + b = 2 a - 2 b$
$b + 2 b = 2 a - a$
$3 b = a$
$3 b = 2 b + 6$
$3 b - 2 b = 6$
$b = 6$

$a = 2 \times 6 + 6$
$a = 18$