# 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 Answers Oct 30, 2017 Let the money in the starting be $x$Then, he spend one half of his money for a book book cost = $\frac{1}{2} x = \frac{x}{2}$And he spend one-third on a pen pen cost =$\frac{1}{3} x = \frac{x}{3}$Now after this,$2.25 is left, we make the equation
x-x/2-x/3=$2.25 We take LCM $\frac{x \times 6 - x \times 3 - x \times 2}{6} = 2.25$$\frac{6 x - 3 x - 2 x}{6} = 2.25$$\frac{x}{6} = 2.25$Transfer 6 to RHS $x = 2.25 \times 6$$13.5
The boy started with $13.5$ 13.5 , hope it helps :)

#### Explanation:

$\frac{x}{2} + \frac{x}{3} = x - 2.25$

$\frac{\text{5x}}{6} = x - 2.25$

$5 x = 6 x - 13.5$

$13.5 = x$

Oct 30, 2017

$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$= \frac{1}{2} x$

While the pen is
pen = $\frac{1}{3} x$

So initially, the boy had $x$ money, then he bought a book for $\frac{1}{2} x$ and a pen for $\frac{1}{3} x$ then he had $2.25 left. In equation form, this would be: $x - \left(\frac{1}{2} x + \frac{1}{3} x\right) = 2.25$$x - \left(\frac{3}{6} x + \frac{2}{6} x\right) = 2 \frac{1}{4}$$x - \frac{5}{6} x = \frac{9}{4}$$\frac{1}{6} x = \frac{9}{4}$$x = \left(\frac{9}{4}\right) \cdot 6$$x = \frac{54}{4}$$x = \frac{27}{2}$$x = 13 \frac{1}{2}$$x = 13.5$So we know that the boy initially had$13.50

Checking:
Book would cost $= \frac{27}{2} \cdot \frac{1}{2} = \frac{27}{4}$
Pen would cost $= \frac{27}{2} \cdot \frac{1}{3} = \frac{27}{6}$
Total cost of purchases
$= \frac{27}{4} + \frac{27}{6}$
$= \frac{81}{12} + \frac{54}{12}$
$= \frac{135}{12} = 11 \frac{1}{4} = 11.25$

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