Chapter 8.3, Problem 59PFA

To determine

To find: The product of their ages.

Answer to Problem 59PFA

  $8x^2+32x+32$

Explanation of Solution

Given:

Bob is twice as old as his sister. The sum of their ages is $6x+12$

Calculation:

Let Bob age is B years and his sister age is S years.

So,

  $B=2S\mathrm{...}\left(i\right)$

And

  $B+S=6x+12$

From equation (i)

  $\begin{array}{c}2S+S=6x+12\\ 3S=6x+12\\ S=\frac{1}{3}\left(6x+12\right)\\ S=2x+4\end{array}$

From equation (i)

  $\begin{array}{c}B+2x+4=6x+12\\ B=4x+8\end{array}$

Thus, product of their ages is given by

  $\begin{array}{l}B\cdot S\\ =\left(4x+8\right)\left(2x+4\right)\\ =8x^2+16x+16x+32\\ =8x^2+32x+32\end{array}$