Chapter 1.4, Problem 29E

To determine

The percent of people are ambidextrous.

Answer to Problem 29E

Number of ambidextrous people is $1\%$ .

Explanation of Solution

Given information:Number of left hander, right handed andambidextrous people are given.

Calculation:let $x$ represent the number of left handed people, $y$ represent the number of right handed people and $z$ represent the number of ambidextrous people.

We know the sum of percent is $100$ .

Set up a system of equations:

  $\begin{array}{l}x+y+z=100(i)\\ x=\frac{1}{10}y(ii)\\ \frac{1}{100}y=9(\frac{1}{100}x+\frac{1}{100}z)(iii)\end{array}$

From equation $(ii)\mathrm{and}(iii)$

  $\begin{array}{l}10x=y(iv)\\ y=900(\frac{x+z}{100})\\ y=9x+9z\\ 9x-y+9z=0(v)\end{array}$

Put $y=10x$ in equation $(i)\mathrm{and}(v)$ we get:

  $\begin{array}{l}x+10x+z=100\\ 11x+z=100(vi)\\ 9x-10x+9z=0\\ 9z=x\end{array}$

Put $x=9z$ in equation $(vi)$ we get $z$ :

  $\begin{array}{l}11(9z)+z=100\\ 99z+z=100\\ 100z=100\\ z=\frac{100}{100}=1\end{array}$

Therefore,number of ambidextrous people is $1\%$ .