A boy spent half his money for a book and one third his money for a pen. The remaining $2.25 he saved. How much money did he have originally?
Let's denote the original amount of money the boy had as "x" dollars.
According to the problem, he spent half of his money on a book, so he spent (1/2)x dollars on the book.
He also spent one-third of his money on a pen, so he spent (1/3)x dollars on the pen.
The total amount of money he spent on the book and the pen is (1/2)x + (1/3)x = (5/6)x dollars.
We know that the remaining amount of money he saved is $2.25, so we can set up the equation (5/6)x = $2.25.
To solve for x, we can multiply both sides of the equation by 6/5: x = 6/5 * $2.25.
Multiplying, we find x = $2.70.
Therefore, the boy originally had $2.70. Answer: \boxed{2.70}.
To solve this problem, we'll use a step-by-step approach.
Let's say the original amount of money that the boy had is represented by the variable "x."
From the given information, we know that the boy spent half of his money on a book. So, he spent 0.5x on the book.
He also spent one-third of his money on a pen. Therefore, he spent (1/3)x on the pen.
The remaining amount of money he saved is $2.25. So, we can write the equation:
x - 0.5x - (1/3)x = 2.25
To solve this equation, we'll combine like terms:
(1 - 0.5 - 1/3)x = 2.25
(0.333)x = 2.25
Now, we'll divide both sides of the equation by 0.333 to isolate x:
x = 2.25 / 0.333
Using a calculator, we find that x ≈ 6.757
Therefore, the boy originally had approximately $6.76.
Let's assume the original amount of money the boy had is "x" dollars.
According to the given information:
- He spent half his money on a book, which is (1/2)x dollars.
- He spent one third of his money on a pen, which is (1/3)x dollars.
- The remaining amount he saved is $2.25.
To find the original amount of money he had, we can set up an equation as follows:
x - [(1/2)x + (1/3)x] = $2.25
First, let's simplify the equation by combining like terms:
x - [(1/6)x] = $2.25
Next, let's find a common denominator for the fractions:
x - [(1/6)x] = $2.25
6x/6 - (1/6)x = $2.25
Now, let's combine the terms:
(6x - x)/6 = $2.25
Simplifying the numerator:
5x/6 = $2.25
To solve for x, we can multiply both sides of the equation by 6:
5x = $2.25 * 6
5x = $13.50
Divide both sides of the equation by 5 to isolate x:
x = $13.50 / 5
x = $2.70
Therefore, the original amount of money the boy had is $2.70.