The ratio of the capacity of Tank A to that of Tank B is 7 : 3.Each tank is filled with some water.If the water from Tank B is poured into Tank A until it reaches the brim,there will be 9 litres of water left in Tank B.If the water from Tank A is poured into Tank B until it reaches the brim,there will be 33 litres of water left in Tank A.How much more water are needed to fill both tanks completely?

Guest Jun 29, 2014

#1**+10 **

Let x be the amount of water in tank A

Let m be the amount of water needed to fill tank A

So the total capacity of tank A is (x+m)

----------------------

Let y be the amount of water in tank B

Let n be the amount of water needed to fill tank B

and the total capacity of tank B is (y+n)

-------------------------

**We are being asked to find (n+m)**

Now the capacity ratio of tank A to tank B is 7:3 so

$$\begin{array}{rll}

\frac{x+m}{y+n}&=&\frac{7}{3}\\\\

3(x+m)&=&7(y+n)\\\\

\end{array}$$

--------------------------

now there is x litres in tank A and m litres are needed to fill tank B so

x-n=33 litres ==> x=33+n

Likewise

y-m=9 lites ==> y=9+m

-----------------------------

$$\begin{array}{rll}

3(x+m)&=&7(y+n)\qquad \mbox{substituting for x and y we get;}\\

3(33+n+m)&=&7(9+m+n)\\

3*33+3(m+n)&=&7*9+7(m+n)\\

99+3(m+n)&=&63+7(m+n)\\

36&=&4(m+n)\\

9&=&m+n\\

\end{array}$$

so the amount of water to fill up both tanks completely is 9L

Melody
Jun 29, 2014

#1**+10 **

Best Answer

Let x be the amount of water in tank A

Let m be the amount of water needed to fill tank A

So the total capacity of tank A is (x+m)

----------------------

Let y be the amount of water in tank B

Let n be the amount of water needed to fill tank B

and the total capacity of tank B is (y+n)

-------------------------

**We are being asked to find (n+m)**

Now the capacity ratio of tank A to tank B is 7:3 so

$$\begin{array}{rll}

\frac{x+m}{y+n}&=&\frac{7}{3}\\\\

3(x+m)&=&7(y+n)\\\\

\end{array}$$

--------------------------

now there is x litres in tank A and m litres are needed to fill tank B so

x-n=33 litres ==> x=33+n

Likewise

y-m=9 lites ==> y=9+m

-----------------------------

$$\begin{array}{rll}

3(x+m)&=&7(y+n)\qquad \mbox{substituting for x and y we get;}\\

3(33+n+m)&=&7(9+m+n)\\

3*33+3(m+n)&=&7*9+7(m+n)\\

99+3(m+n)&=&63+7(m+n)\\

36&=&4(m+n)\\

9&=&m+n\\

\end{array}$$

so the amount of water to fill up both tanks completely is 9L

Melody
Jun 29, 2014