Question

Daniel spent 2/5 of his money on books, 1/3 of the remaining money on food and he has left with $28. How much money did he have before the shopping?

Answer 1

Answer:

Daniel had total $70 before shopping.

Step-by-step explanation:

Let us assume that Daniel had total money before shopping = $x.

He spent $\frac{2}{5}$  of total money on books, that is = $$\frac{2}{5}$  of x= $\frac{2}{5}$  x.

Remaining money with him = (x-$\frac{2}{5}$ x) .

And spent 1/3 of the remaining that is 1/3 of (x-2/5x)  = 1/3(x-$\frac{2}{5}$ x) on food.

Money left with him = $28.

Therefore, we can setup and equation.

Money spent on books + Money spent on food + Remaining money = Total money  before shopping.

Substituting above values in equation, we get

$\frac{2}{5}$  x +   $\frac{1}{3}$(x-$\frac{2}{5}$ x) + 28 = x.

Subtracting x-$\frac{2}{5}$ x = $\frac{5x}{5}$ - $\frac{2x}{5}$ = $\frac{3x}{5}$, we get

$\frac{2}{5}$ x +  $\frac{1}{3}$($\frac{3x}{5}$) + 28 = x.

Multiplying $\frac{1}{3}$($\frac{3x}{5}$), we get $\frac{x}{5}$

Therefore,

$\frac{2}{5}$ x +$\frac{x}{5}$+28=x

$\frac{3}{5}$ x +28 =x.

Subtracting $\frac{3}{5}$ on both sides, we get

$\frac{3}{5}$ x + 28-$\frac{3}{5}$ x =x-$\frac{3}{5}$ x

28 =  $\frac{5x}{5}$ - $\frac{3x}{5}$

28 = $\frac{2x}{5}$.

Multiplying both sides by 5, we get

28×5 = 5×$\frac{2x}{5}$.

140 =2x.

Dividing both sides, by 2, we get

$\frac{140}{2}=\frac{2x}{2}$

x=70.

Therefore, Daniel had total $70 before shopping.