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?
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)
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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)
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We are being asked to find (n+m)
Now the capacity ratio of tank A to tank B is 7:3 so
$$\begin{array}{rll}
\frac{x+m}{y+n}&=&\frac{7}{3}\\\\
3(x+m)&=&7(y+n)\\\\
\end{array}$$
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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
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$$\begin{array}{rll}
3(x+m)&=&7(y+n)\qquad \mbox{substituting for x and y we get;}\\
3(33+n+m)&=&7(9+m+n)\\
3*33+3(m+n)&=&7*9+7(m+n)\\
99+3(m+n)&=&63+7(m+n)\\
36&=&4(m+n)\\
9&=&m+n\\
\end{array}$$
so the amount of water to fill up both tanks completely is 9L
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