# One number is four times another number. If the smaller number is subtracted from the larger number, the result is the same as as if the smaller number were increased by 30. What are the two numbers?

$a = 60$
$b = 15$

#### Explanation:

Larger number = a
Smaller number = b

$a = 4 b$
$a - b = b + 30$

$a - b - b = 30$
$a - 2 b = 30$
$4 b - 2 b = 30$
$2 b = 30$
$b = \frac{30}{2}$

$b = 15$

$a = 4 \times 15$

$a = 60$