Question

d. 45.8 8. There are three brothers in the Howard family. Darris, Miles, and Alan, whose ages add up to 48 years. Darris is twice as old as Miles, and Alan is 3 years older than Darris. Use any strategy, such as a tape diagram or equation, to find the age of each brother. Show your work Miles is 9 years old. Darris is 18 years old. Alan is 21 years old.

Answer 1

Given data:

The expression for the total age of Darris, Miles, and Alan is D+M+A= 48 years.

The expression for Darris is twice as old as Miles is D=2M or M=D/2.

The expression for Alan is 3 years older than Darris is A=D+3.

Substitute (D/2) for M, and (D+3) for A in the first equation.

$\begin{gathered} D+\frac{D}{2}+D+3=48 \\ 2D+\frac{D}{2}=45 \\ \frac{5D}{2}=45 \\ 5D=90 \\ D=18\text{ years} \end{gathered}$

The Miles age is,

$\begin{gathered} M=\frac{18}{2}\text{ years} \\ =9\text{ years} \end{gathered}$

The Alan age is,

$\begin{gathered} A=(18\text{ years)+3 years} \\ =21\text{ years} \end{gathered}$

Thus, the Dorris age is 18 years, Miles age is 9 years, and Alan age is 21 years.