Question

Vector makes three different purchases at three different stores one afternoon. Each time he spends 1/3 of the money he is carrying. If he ends the day with $16 how much money did he have at the end of the day?

Answer 1

The money which vector have is $54

Explanation:

Given as:

Vector makes three different purchases at three different stores one afternoon. Each time he spends 1/3 of the money he is carrying.

At The end of day vector have money left = $16

Let the money does Vector have at start = $x

Now, According to question

At The first store he had money with him = $x

So, After purchased of item, The money left with him = $x - $
`(x)/(3)` = $
`(2x)/(3)`

At The second store he had money with him = $
`(2x)/(3)`

So, After purchased of item, The money left with him = $
`(2x)/(3)` - $
`(2x)/(9)` = $
`(4x)/(9)`

At The third store he had money with him = $
`(4x)/(9)`

So, After purchased of item, The money left with him = $
`(4x)/(9)` - $
`(4x)/(27)` = $
`(8x)/(27)`

Now, Again

∵ At The day end the money left with Vector = $16

So, $
`(8x)/(27)` = $16

Or. 8 x = $16 × 27

∴ x =
`(16* 27)/(8)`

i.e x = $54

So, The money which vector have = x = $54

Hence, The money which vector have is $54 Answer