Question

The sum of two numbers is 4500. If 10% of one number is 12.5% of the other, find the numbers.

Answer 1

Let the two numbers be x and y, where x + y = 4500. The condition states:

10% of x = 12.5% of y

Step 1: Express the percentages as fractions

`10/100x = 12.5/100y`

Simplify the fractions: `1/10x=1/8y`

Multiply through by 80 (LCM of 10 and 8) to eliminate fractions:

8x = 10y

Step 2: Relate x and y

`x = 10/8y = 5/4 y`

From 8x = 10y, solve for x in terms of y:

`x=10/8 y = 5/4 y`

Step 3: Use the sum condition

Substitute `x=5/4y` into x+y = 4500:

`5/4 y+y = 4500`

Combine terms: `5/4y+4/4y=4500`

Multiply through by 4: 9y = 18000

Solve for y: `y = 18000/9 = 2000`

Using x + y = 4500

x = 4500 − y = 4500 − 2000 = 2500

x = 2500 and y = 2000