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

Daniel had total $70 before shopping.

Explanation:

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

He spent
`(2)/(5)` of total money on books, that is = $
`(2)/(5)` of x=
`(2)/(5)` x.

Remaining money with him = (x-
`(2)/(5)` x) .

And spent 1/3 of the remaining that is 1/3 of (x-2/5x) = 1/3(x-
`(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

`(2)/(5)` x +
`(1)/(3)`(x-
`(2)/(5)` x) + 28 = x.

Subtracting x-
`(2)/(5)` x =
`(5x)/(5)` -
`(2x)/(5)` =
`(3x)/(5)`, we get

`(2)/(5)` x +
`(1)/(3)`(
`(3x)/(5)`) + 28 = x.

Multiplying
`(1)/(3)`(
`(3x)/(5)`), we get
`(x)/(5)`

Therefore,

`(2)/(5)` x +
`(x)/(5)`+28=x

`(3)/(5)` x +28 =x.

Subtracting
`(3)/(5)` on both sides, we get

`(3)/(5)` x + 28-
`(3)/(5)` x =x-
`(3)/(5)` x

28 =
`(5x)/(5)` -
`(3x)/(5)`

28 =
`(2x)/(5)`.

Multiplying both sides by 5, we get

28×5 = 5×
`(2x)/(5)`.

140 =2x.

Dividing both sides, by 2, we get

`(140)/(2)=(2x)/(2)`

x=70.

Therefore, Daniel had total $70 before shopping.