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 = 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

$ 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

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 = 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