Gill won certain prize money in a cooking competition. She spent half price money on clothes and one third on crockery and gave the remaining 2000 rupees an orphanage. how much money did she win?
Given: Gill won a cooking competition.
$\frac{1}{2}$ spent on clothes
$\frac{1}{3}$ spent on crockery
Rs 2000 donated in to orphanage
To do: Find the prize money won by her.
Solution:
Lets take the prize money won =Rs $x$
Half the prize money spent on clothes,
Money spent on clothes = Rs$\frac{ x}{2}$
one third of prize money spent on crockery,
Money spent on crockery = Rs$\frac{x}{3} $
Money given to orphanage = Rs 2000
Total prize money = Money spent on clothes $+$ Money spent on crockery $+$ Money given to orphanage
$x = \frac{ x }{ 2} + \frac{ x}{ 3 } + 2000$
Now bring all variables(x) on the same side,
$ x - \frac{x }{ 2} - \frac{x }{ 3} = 2000$
Denominators are different,
to make them equal , take LCM
LCM of 2 , 3 is 6
$\frac{x \times 6 }{ 1 \times 6} = \frac{6 x }{ 6}$
$\frac{x \times 3 }{ 2 \times 3} = \frac{3 x }{ 6}$
$\frac{x \times 2 }{ 3 \times 2} = \frac{2 x }{ 6}$
$\frac{6 x }{ 6}-\frac{3 x }{ 6}-\frac{2 x }{ 6}$ =2000
$\frac{6x-3x2x}{6}$=2000
$\frac{x}{6} =2000$
$x= 2000\times 6$
$x= 12000 $
Therefore, Gill won Rs 12000
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