Question

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?

Answer 1

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`

`4/100a+7/100b = 48`

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

`4a+7b=4800`

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

`4a+4b=3600`

Subtracting these equations from one another, we find:

`3b=1200`

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

`b=400`

Then:

`a = 900-b = 900-400 = 500`