Chapter 1.8, Problem 68E

a .

To determine

To write: composite function that gives the youngest sibling’s age in terms of the oldest.

Answer to Problem 68E

  $Y\left(M\left(O\right)\right)=O-12$

Explanation of Solution

Given:

The oldest is twice the age of the middle sibling, and the middle sibling is six years older than one-half the age of the youngest.

Calculation:

Let O represents the age of the oldest sibling, M represents the age of the middle sibling and Y represents the youngest sibling.

Now the oldest is twice the age of the middle sibling, or it can be said that the age of the middle sibling is half the age of the oldest.

  $M\left(O\right)=\frac{1}{2}O$

And the middle sibling is six years older than one-half the age of the youngest or it can be said that the age of the youngest is twice of six minus the age of middle sibling.

  $Y\left(M\right)=2\left(M-6\right)$ ….. (2)

Thus,

  $\begin{array}{c}\left(Y\circ M\right)\left(O\right)=Y\left(M\left(0\right)\right)\\ =Y\left(\frac{1}{2}O\right)\\ =2\left(\frac{1}{2}O-6\right)\\ =O-12\end{array}$

b.

To determine

To find: Age of the middle and the oldest sibling, given that the youngest sibling is 2 years old.

Answer to Problem 68E

Middle sibling is 7 years old and the oldest sibling is 14 years old

Explanation of Solution

Calculation:

From part (a),

  $\begin{array}{c}Y\left(M\right)=2\left(M-6\right)\\ 2=2\left(M-6\right)\\ 1=M-6\\ M=7\end{array}$

And

  $\begin{array}{c}Y\left(M\left(O\right)\right)=O-12\\ 2=O-12\\ O=2+12\\ O=14\end{array}$

So, Middle sibling is 7 years old and the oldest sibling is 14 years old.