Question

Mrs Wright spent 2/9 of her paycheck on food and 1/3 on rent. She spent 1/4 of the remainder on transportation. She had $210 left. How much was Mrs. Wright’s paycheck ?

Answer 1

Mrs Wright's paycheck was $ 630

Solution:

Given that,

Mrs Wright spend on food = $\frac{2}{9}$

Fraction spent on rent = $\frac{1}{3}$

She spent 1/4 of the remainder on transportation

Remaining left with her = $ 210

Let the paycheck amount be "n"

Now, we know that, paycheck amount = used amount + left over amount

Here, left over amount = 210

Paycheck amount = 2/9 of paycheck on food + 1/3 of paycheck on rent + 1/4 of remainder on transportation + 210

$n=\frac{2}{9} n+\frac{1}{3} n+\frac{1}{4}\left(n-\frac{2}{9} n-\frac{1}{3} n\right)+210$

Upon simplifying we get,

$n=\frac{2}{9} n+\frac{3}{9} n+\frac{1}{4} n\left(1-\frac{2}{9}-\frac{3}{9}\right)+210$

$n=\left(\frac{2}{9}+\frac{3}{9}\right) n+\frac{1}{4} n\left(1-\frac{(2+3)}{9}\right)+210$

On simplification, we get

$n=\frac{5}{9} n+\frac{1}{4} n \times \frac{4}{9}+210$

$\mathrm{n}=\frac{5}{9} \mathrm{n}+\frac{1}{9} \mathrm{n}+210$

On adding fractions we get,

$\begin{array}{l}{\mathrm{n}=\frac{6}{9} \mathrm{n}+210} \\\\ {\mathrm{n}-\frac{2}{3} \mathrm{n}=210} \\\\ {\frac{1}{3} \mathrm{n}=210} \\\\ {\mathrm{n}=3 \times 210=630}\end{array}$

Hence, the paycheck amount is $630