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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?

Respuesta :

tramserran

Answer: lived 48 years

              reigned for 15 years

Step-by-step 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:

 [tex].\quad x+9=\dfrac{1}{2}y\\\\\underline{-x+9}=\underline{-\dfrac{1}{8}}y\\\\.\qquad 18=\dfrac{3}{8}y\\\\.\qquad 48=y[/tex]  

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

[tex].\quad x+9=\dfrac{1}{2}(48)\\\\.\quad x+9 = 24\\\\.\qquad x = 15[/tex]    

             

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