Chapter 1.5, Problem 13IP

To determine

What was the amount of lawanda’s paycheck.

Answer to Problem 13IP

  $\$119$

Explanation of Solution

Given :

Lawanda put $15 of her paycheck in saving. Then she spent one half of what was left on clothes. She paid $24 for a concert ticket and later spent one half of what was then left on a book, when she got home she had $14 left.

In order to find what was the amount of lawanda’s paycheck, let T be the total amount of paycheck, then adding the amount of saving, (that is $15), amount of spent on clothes, (that is 1/2 of T minus amount of saving,) amount spent on concert ticket, (that is $24,) amount spent on book,( that is 1/2 of Tminus saving minus amount spent on clothes minus spent on concert), and then the left amount, that is $14 as shown below:

  $\begin{array}{l}\text{T}=15+\left(\frac{1}{2}\right)\left(\text{T}-15\right)+24+\left(\frac{1}{2}\right)\left[\left(\text{T}-15-\left(\frac{1}{2}\right)\left(\text{T}-15\right)\right)-24\right]+14\\ \text{distributing and cobining terms}\\ \text{15+}\frac{\text{T}}{2}-7.5+24+\frac{\text{T}}{2}-7.5-\frac{\text{T}}{4}+\frac{15}{4}-12+14=\text{T}\\ \text{T}=29.75+0.75\text{T}\\ \text{T}-0.75\text{T}=29.75+0.75\text{T}-0.75\text{T}\\ \text{0}\text{.25T}=29.75\\ \frac{0.25\text{T}}{0.25}=\frac{29.75}{0.25}\\ \text{T}=119\end{array}$

So, lawanda’s paycheck has $119.