Chapter 3.4, Problem 21P

A grandmother says her grandson is two years older than her granddaughter and that together, they are at least 12 years old. How old are her grandson and granddaughter?

To determine

To calculate: The age of the granddaughter and grandson.

Answer to Problem 21P

The age of granddaughter is more than or equal to 5 years and age of grandson is more than or equal to 7 years.

Explanation of Solution

Given information: The grandson is 2 years older than the granddaughter and together they are at least 12 years old.

Calculation:

Let, the age of granddaughter be x years.

The grandson is 2 years older than her.

$\therefore$ The age of grandson = $(x+2)$ years.

Total age of them is

$\begin{array}{l}x+(x+2)\\ =2x+2\end{array}$

Together they are at least 12 years old.

$\therefore$ It can be written as,

$\begin{array}{l}2x+2\ge 12\\ \Rightarrow 2x\ge 12-2\\ \Rightarrow 2x\ge 10\\ \Rightarrow x\ge \frac{10}{2}\\ \therefore x\ge 5\end{array}$

$\therefore (x+2)=5+2=7$

So, the age of granddaughter is more than or equal to 5 years and the age of grandson is more than or equal to 7 years.