Question

The sum of two numbers is 4 times their difference. If one exceeds the other by 8, what are the numbers?

Answer 1

12, 20

Explanation:

Let the two numbers be x and y, where x > y

According to the given information:

x + y = 4(x - y)

x + y = 4x - 4y

y + 4y = 4x - x

5y = 3x

`y = (3)/(5)x.... (1)`

Since, one number exceeds the other by 8.

`\implies x = y + 8\\\\</p><p>\implies y = x - 8.....(2)\\\\`

From equations (1) & (2)

`x - 8 = (3)/(5) x \\ \\ 5(x - 8) = 3x \\ \\ 5x - 40 = 3x \\ \\ 5x - 3x = 40 \\ \\ 2x = 40 \\ \\ x = (40)/(2) \\ \\ \huge \purple{ \boxed{\implies x = 20}} \\ \\ \implies \: y = x - 8 = 20 - 8 \\ \\ \huge \pink{ \boxed{ \implies \: y = 12}}`