Chapter 8.1, Problem 69PFA

To determine

To write an expression for the sum of the ages after 5 years from now.

Answer to Problem 69PFA

  $x^2+2x+9$

Explanation of Solution

Given:

Age of the child: $2x-5$

Age of her mother: $x^2+4$

Calculation:

The present age of child is $2x-5.$

The present age of her mother is $x^2+4.$

After 5 years, the age of the child and mother will be 5 more than their present ages.

The age of child after five years is five more than the present age of the child.

  $\Rightarrow (2x-5)+5$

Simplifying,

  $\begin{array}{l}\Rightarrow 2x-5+5\\ \Rightarrow 2x\end{array}$

The age of the child’s mother after five years is five more than the present age of her mother.

  $\Rightarrow (x^2+4)+5$

Simplifying,

  $\begin{array}{l}\Rightarrow x^2+4+5\\ \Rightarrow x^2+9\end{array}$

The sum of the ages of the child and her mother after five years is,

  $\begin{array}{l}\Rightarrow (2x)+(x^2+9)\\ \Rightarrow x^2+2x+9\end{array}$

Conclusion:

The sum of the ages of the child and her mother after five years is $x^2+2x+9.$