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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

Best Answer 

 #1
avatar+91436 
+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
Sort: 

3+0 Answers

 #1
avatar+91436 
+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
 #2
avatar+80874 
0

Very nice, Melody!!! That was a tough one !!!

3 points from me.....

 

CPhill  Jun 29, 2014
 #3
avatar+91436 
0

Thank you Chris,  we do make a good pair of colourful eggs.   ♬  

Melody  Jun 29, 2014

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