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