Question

8. There are three brothers in the Howard family, Daryl, Malik, and Terrance, whose ages add up to 26 years. Daryl is 3 times as old as Malik, and Terrance is 5 years older than Daryl.Use any strategy, such as a tape diagram or equation, to find the age of each brother. Show your work.

Answer 1

ANSWER:

Daryl: 9 years old

Malik: 3 years old

Terrance: 14 years old

STEP-BY-STEP EXPLANATION:

Let D be Daryl's age, M be Malik's age and T be Terrance's age, we can establish the following system of equations:

$\begin{gathered} D+M+T=26 \\ \\ D=3M \\ \\ T=D+5 \end{gathered}$

We solve the system as follows:

$\begin{gathered} \text{ We substitute the third equation in the first one, just like this:} \\ \\ D+M+D+5=26 \\ \\ \text{ We replace the second equation in this new equation obtained, just like this:} \\ \\ 3M+M+3M+5=26 \\ \\ 7M=26-5 \\ \\ M=\frac{21}{7} \\ \\ M=3 \\ \\ \text{ Now, we calculate Daryl's age} \\ \\ D=3M=3\cdot3 \\ \\ D=9 \\ \\ \text{ Finally, we calculate the age of Terrance} \\ \\ T=9+5 \\ \\ T=14 \end{gathered}$

This means that Daryl is 9 years old, Malik is 3 years old and Terrance is 14 years old.