Question

Math problem: If Alexander the Great had lived 9 years more his reign would have lasted 1/2 his life, while if he had lived 9 years less his reign would have lasted 1/8 of his life. How old was Alexander when he died? And how long did he reign?

Answer 1

Answer: lived 48 years

reigned for 15 years

Explanation:

Let x represent the number of years he reigned.

Let y represent Alexander's age.

Use the given information to create a system of equations:

Equation 1: x + 9 = (1/2)y

Equation 2: x - 9 = (1/8)y

Multiply the second equation by -1 and add the equations to eliminate x:

`.\quad x+9=(1)/(2)y\\\\\underline{-x+9}=\underline{-(1)/(8)}y\\\\.\qquad 18=(3)/(8)y\\\\.\qquad 48=y`

Input y = 48 into either equation to solve for x:

`.\quad x+9=(1)/(2)(48)\\\\.\quad x+9 = 24\\\\.\qquad x = 15`