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?

(3/6)x + (2/6)x + 2.25 = x

To find out how much money the boy had originally, we can work backwards. Let's start by finding the fractional parts of his money that he spent on the book and the pen.

We know that he spent one-half of his money on a book, which is equal to 1/2 of his original amount. And he spent one-third of his money on a pen, which is equal to 1/3 of his original amount.

Let's assume the original amount of money he had is 'x' dollars.

The amount he spent on the book = (1/2) * x
The amount he spent on the pen = (1/3) * x

The remaining money he saved is given as $2.25, so we can set up an equation:

x - [(1/2) * x + (1/3) * x] = $2.25

Now let's solve this equation to find the value of 'x'.

First, simplify the fraction parts:

x - (3/6)x - (2/6)x = $2.25

Combine like terms:

x - (5/6)x = $2.25

[(6/6) - (5/6)]x = $2.25

(1/6)x = $2.25

To isolate 'x', multiply both sides of the equation by 6:

x = $2.25 * 6

x = $13.50

Therefore, the boy originally had $13.50.