Respuesta :
Mrs Wright's paycheck was $ 630
Solution:
Given that,
Mrs Wright spend on food = [tex]\frac{2}{9}[/tex]
Fraction spent on rent = [tex]\frac{1}{3}[/tex]
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
[tex]n=\frac{2}{9} n+\frac{1}{3} n+\frac{1}{4}\left(n-\frac{2}{9} n-\frac{1}{3} n\right)+210[/tex]
Upon simplifying we get,
[tex]n=\frac{2}{9} n+\frac{3}{9} n+\frac{1}{4} n\left(1-\frac{2}{9}-\frac{3}{9}\right)+210[/tex]
[tex]n=\left(\frac{2}{9}+\frac{3}{9}\right) n+\frac{1}{4} n\left(1-\frac{(2+3)}{9}\right)+210[/tex]
On simplification, we get
[tex]n=\frac{5}{9} n+\frac{1}{4} n \times \frac{4}{9}+210[/tex]
[tex]\mathrm{n}=\frac{5}{9} \mathrm{n}+\frac{1}{9} \mathrm{n}+210[/tex]
On adding fractions we get,
[tex]\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}[/tex]
Hence, the paycheck amount is $630
