On Monday

On Monday, Jason used 2/7 of his money to buy a book. On Tuesday, he used 1/2 of his money to buy a toy.
If he has 6 dollars left, how much money he has in the beginning? What fraction of money is left?
 

Correct answer:

a =  16.8 USD
b =  5/14

Step-by-step explanation:

$$\begin{gathered} X=\frac{2}{7}\doteq 0.2857 \\ Y=\frac{1}{2}\cdot (1-X)=\frac{1}{2}\cdot (1-\frac{2}{7})=\frac{5}{14}\doteq 0.3571 \\ s=X+Y=\frac{2}{7}+\frac{5}{14}=\frac{4}{14}+\frac{5}{14}=\frac{4+5}{14}=\frac{9}{14}\doteq 0.6429 \\ b=1-s=1-\frac{9}{14}=\frac{1\cdot 14}{14}-\frac{9}{14}=\frac{14}{14}-\frac{9}{14}=\frac{14-9}{14}=\frac{5}{14}\doteq 0.3571 \\ 6=b\cdot a \\ 6=0.35714285714286\cdot a \\ 0.357143a=6 \\ a=\frac{6}{0.35714286}=16.8 \\ a=\frac{84}{5}=16.8=\frac{84}{5}\text{USD}=16.8\text{USD} \end{gathered}$$

$b=\frac{5}{14}=0.3571$

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