Question

A boy spent one-half of his money for a book and one-third of his money for a pen. The remaining $2.25 he saved. How much money did he have originally?

Answer 1

Let the money in the starting be `x`
Then, he spend one half of his money for a book
book cost = `1/2x=x/2`
And he spend one-third on a pen
pen cost =`1/3x=x/3`
Now after this, $2.25 is left, we make the equation
`x-x/2-x/3=$2.25`
We take LCM
`(x xx 6- x xx 3 - x xx 2)/6=2.25`
`(6x-3x-2x)/6=2.25`
`x/6=2.25`
Transfer 6 to RHS
`x=2.25 xx 6`
`$13.5`
The boy started with $13.5

Answer 2

$ 13.5 , hope it helps :)

Explanation:

`x/2+x/3=x-2.25`

`"5x"/6=x-2.25`

`5x=6x-13.5`

`13.5=x`

Answer 3

$13.50

Explanation:

Given:
- The book costs half of his money
- The pen costs one-third of his money
- He has $2.25 left

In this case, let `x` be the total money he had prior to his purchases.

So if the book costs half of his money then we can say that
book`= 1/2 x`

While the pen is
pen = `1/3 x`

So initially, the boy had `x` money, then he bought a book for `1/2 x` and a pen for `1/3 x` then he had $2.25 left. In equation form, this would be:

`x - (1/2 x + 1/3 x) = 2.25`
`x - (3/6 x + 2/6 x) = 2 1/4`
`x - 5/6 x = 9/4`
`1/6 x = 9/4`
`x = (9/4) * 6`
`x = 54/4`
`x = 27/2`
`x = 13 1/2`
`x = 13.5`

So we know that the boy initially had $13.50

Checking:
Book would cost `= 27/2 * 1/2 = 27/4`
Pen would cost `= 27/2 * 1/3 = 27/6`
Total cost of purchases
`= 27/4 + 27/6`
`= 81/12 + 54/12`
`= 135/12 = 11 1/4 = 11.25`

So if initially he had $13.50, then
$13.50 - $11.25 = $2.25