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 = 12x=x2
And he spend one-third on a pen
pen cost =13x=x3
Now after this, $2.25 is left, we make the equation
xx2x3=$2.25
We take LCM
x×6x×3x×26=2.25
6x3x2x6=2.25
x6=2.25
Transfer 6 to RHS
x=2.25×6
$13.5
The boy started with $13.5

$ 13.5 , hope it helps :)

Explanation:

x2+x3=x2.25

5x6=x2.25

5x=6x13.5

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=12x

While the pen is
pen = 13x

So initially, the boy had x money, then he bought a book for 12x and a pen for 13x then he had $2.25 left. In equation form, this would be:

x(12x+13x)=2.25
x(36x+26x)=214
x56x=94
16x=94
x=(94)6
x=544
x=272
x=1312
x=13.5

So we know that the boy initially had $13.50

Checking:
Book would cost =27212=274
Pen would cost =27213=276
Total cost of purchases
=274+276
=8112+5412
=13512=1114=11.25

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