
Fraction problems
Hey i was looking for help on these problems; how would i go about finding the solutions to them both?
1.If a storage tank is holding 450 liters when it is three quarters full, how much will it contain when it is two thirds full?.
And
2.three people P,Q and R contribute to a fund. P provides 3/5 of the total, Q provides 2/3 of the remainder and R provides £8. determine a) the total of the fund. b)the contributions of P and Q.
Thanks

1)
Let the total capacity of the tank be $\displaystyle x$.
When it's $\displaystyle \frac{3}{4}$ full it can contain 450 liters.
Now lets find its total capacity. If $\displaystyle \frac{3x}{4}=450$ then $\displaystyle x=\frac{4.450}{3}=600$
So when it's $\displaystyle \frac{2}{3}$ full, there will be $\displaystyle \frac{2.600}{3}=400$ liters.

2)
$\displaystyle Total=x$
P provies $\displaystyle \frac{3}{5}$ of total which is $\displaystyle \frac{3x}{5}$, now the remaining is $\displaystyle x\frac{3x}{5}=\frac{2x}{5}$.
Q provides $\displaystyle \frac{2}{3}$ of the remainder, so $\displaystyle \frac{2x}{5}.\frac{2}{3}=\frac{4x}{15}$ that is the amount Q gives.
R gives 8£, it's equal to $\displaystyle \frac{2x}{15}$.
($\displaystyle \frac{2x}{5}\frac{4x}{15}=\frac{2x}{15}$)
I substracted the amount Q provided ($\displaystyle \frac{4x}{15}$) from the total fund left ($\displaystyle \frac{2x}{5}$) after P's contribution.
So we know that 8£$\displaystyle =\frac{2}{15}$ of the total amount. $\displaystyle 8.\frac{15}{2}=$60£ is the total amount.
From here we can find P's contribution which is $\displaystyle 60.\frac{3}{5}=$36£ and Q's, $\displaystyle 60.\frac{4}{15}=$16£

Thanks mate, that made a lot more sense then the way i was going about it.