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 ?

Mrs Wright's paycheck was $ 630Solution: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 transportationRemaining left with her = $ 210Let the paycheck amount be "n"Now, we know that, paycheck amount = used amount + left over amount Here, left over amount = 210Paycheck 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