# The sum of two numbers is 900. When 4% of the larger is added to 7% of the smaller, the sum is 48. How do you find the numbers?

May 14, 2016

The two numbers are $500$ and $400$

#### Explanation:

Suppose the numbers are $a$ and $b$ with $a > b$

Since "percent" menas "per-hundred" we can understand the facts we are given as:

$a + b = 900$

$\frac{4}{100} a + \frac{7}{100} b = 48$

Multiply both sides of the second equation by $100$ to find:

$4 a + 7 b = 4800$

Multiply both sides of the first equation by $4$ to get:

$4 a + 4 b = 3600$

Subtracting these equations from one another, we find:

$3 b = 1200$

Dividing both sides of this equation by $3$ we get:

$b = 400$

Then:

$a = 900 - b = 900 - 400 = 500$