# Samina spent 1/8 of her money to buy books, 1/5 in purchasing clothes and 1/10 on charity. If she...

## Question:

Samina spent {eq}\frac{1}{8} {/eq} of her money to buy books, {eq}\frac{1}{5} {/eq} in purchasing clothes and {eq}\frac{1}{10} {/eq} on charity.

If she still had {eq}Rs.15 {/eq}, more than half of her money, find the amount she had originally

## Algebraic Equations:

Algebraic formulations can help you model situations and solve problems to find the unknown. The unknown number is usually taken as {eq}x {/eq}.

Samina spent {eq}\dfrac{1}{8}^{th} {/eq} to buy books, {eq}\dfrac{1}{5}^{th} {/eq} for clothes and {eq}\dfrac{1}{10}^{th} {/eq} for charity.

Still, she has {eq}15 {/eq} more than half of the initial amount left.

Let's say Samina had {eq}x {/eq} Rs. initially.

So, the algebraic equation we get here is as follows...

{eq}x-(\dfrac{x}{8}+\dfrac{x}{5}+\dfrac{x}{10})=\dfrac{x}{2}+15 {/eq}

{eq}x(1-\dfrac{1}{2}-\dfrac{1}{8}-\dfrac{1}{5}-\dfrac{1}{10})=15\\ x\left(1-\dfrac{(8\cdot5\cdot10+2\cdot5\cdot10+2\cdot8\cdot10+2\cdot5\cdot8)}{2\cdot5\cdot8\cdot10}\right)=15\\ x\left(1-\dfrac{(400+100+160+80)}{800}\right)=15\\ x\left(1-\dfrac{740}{800}\right)=15\\ x(1-0.925)=15\\ \therefore{x}=\dfrac{15}{0.075}=200 {/eq}

So the original amount that Samina had with her was {eq}200 {/eq} Rs.
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