Chapter 8.1, Problem 75CCR

To determine

Find the age of each of them when Gabriel is twice as old as Elias.

Answer to Problem 75CCR

Gabriel will be 20 years and Elias will be 10 years when Gabriel is twice as old as Elias.

Explanation of Solution

Given:

Gabriel is 12 years old, and his younger brother Elias is 2 years old. How old will each of them be when Gabriel is twice as old as Elias?

Concept Used:

Gabriel is 12 years old, and his younger brother Elias is 2 years old.

Let after x years Gabriel will be twice as old as Elias.

After x years, the age of Gabriel is (12 + x ) years and age of Elias is (2 + x) years.

The required equation: $12+x=2(2+x)$

Calculation:

The required equation: $12+x=2(2+x)$

Solve for x:

  $\begin{array}{l}12+x=2(2+x)\\ 12+x=4+2x\text{[}\text{Distribute with 2]}\\ 12+x-x=4+2x-x\text{[ Subtract x from both sides ] }\\ 12=4+x\\ 12-4=4-4+x\text{[ Subtract 4 from both sides ]}\\ 8=x\Rightarrow x=8\end{array}$

After 8 years Gabriel will be twice as old as Elias.

After 8 years, the age of Gabriel is 20 years and age of Elias is 10 years.

Thus, Gabriel will be 20 years and Elias will be 10 years when Gabriel is twice as old as Elias.