Chapter 1.5, Problem 95E

a.

To determine

To calculate:

Composite function which gives the youngest siblings age in terms of the oldest.

Answer to Problem 95E

The expression for the youngest siblings age in terms of the oldest siblings age is $C=A-12$ .

Explanation of Solution

Give information:

Three siblings of different ages.

Oldest sibling is twice the age of the middle siblings and middle sibling is six years older than one half age of the youngest.

Calculation:

Let the $A,B,C$ be three siblings of decreasing ages.

  $A=2B,B=\frac{1}{2}C+6$

For finding out Composite function which gives the youngest siblings age in terms of the oldest.

First find expression for $C$ in terms of $B$ ,

  $\begin{array}{l}B=\frac{1}{2}C+6\\ \frac{1}{2}C=B-6\end{array}$

Multiply each side of the equation by $2$

  $C=2B-12$

Now substitute $B=\frac{A}{2}$ in above expression,

  $\begin{array}{l}C=2\left(\frac{A}{2}\right)-12\\ =A-12\end{array}$

Therefore, the expression for the youngest siblings age in terms of the oldest siblings age is $C=A-12$ .

b.

To determine

To calculate:

Ages of two other siblings.

Answer to Problem 95E

The age of middle child is $7years$ old and the age of the oldest child is $14years$ old.

Explanation of Solution

Give information:

Youngest sibling is two years old.

Calculation:

For finding out the ages of the other two siblings if the youngest sibling is two years old.

  $\begin{array}{l}B=\frac{1}{2}C+6\\ B=\frac{1}{2}\left(2\right)+6\\ B=1+6\\ B=7\end{array}$

And,

  $\begin{array}{l}A=2B\\ A=2\left(7\right)\\ A=14\end{array}$

Thus, the age of middle child is $7years$ old and the age of the oldest child is $14years$ old.