Chapter 1.5, Problem 95E

a .

To determine

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

Answer to Problem 95E

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

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,

  $O\left(M\right)=2M$ ….. (1)

And the middle sibling is six years older than one-half the age of the youngest.

  $M\left(Y\right)=\frac{1}{2}Y+6$ ….. (2)

Thus,

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

b.

To determine

To find: Age of the middle and the younger sibling, given that the older sibling is 16 years old.

Answer to Problem 95E

Middle sibling is 8 years old and the younger sibling is 4 years old

Explanation of Solution

Calculation:

From part (a),

  $\begin{array}{c}O\left(M\right)=2M\\ 16=2M\\ M=8\end{array}$

And

  $\begin{array}{c}\left(O\circ M\right)\left(Y\right)=Y+12\\ 16=Y+12\\ Y=16-12\\ Y=4\end{array}$

So, Middle sibling is 8 years old and the younger sibling is 4 years old.