fractions & percent problem

[knyc]

Can someone help explain the way they answer this question?

[Deleted because poster did not cite author.]


Many thanks.

[rschunti]

is the answer 10/3 gallons?

[knyc]

but how did you get to 10/3?

Does anyone else try it and get a different answer?

[rohit801]

let's say the capacity is C gallons. we know that bucket is half full. there must be some gallons in there, say x gallons.
hence, x = C/2, right?

now, If he adds 2/3 gallon, it will be filled to 70% capacity means:

x + 2/3 = 0.7 C [x was already in there; we added 2/3 and that makes up 70% of the capacity]
subsitute x = C/2 and you'll get C=10/3 gallons...

helps?

[rschunti]

Let say total capacity be "X"
According to question it is initially half filles which is =X/2----------1
Then 2/3 gallon of water/liquid added totalling=(X/2)+(2/3)----------2

According to question equation number 2 will be 70% of total capacity whch is X
Hence following will be equation:-

(X/2)+(2/3)=(70/100)(X)---------------------3

upon solving equation (2)
X=10/3 gallons.

[knyc]

thanks so much you guys.
obviously you get the fractions into their lowest common denominators to solve for x, right?

[brian]

Moving to LCD's is one clear path to take -- some people also like converting the fractions into "easier-to-use" whole numbers. But either approach would get you to the same end result.
Thanks.
-Brian lange

[knyc]

Thanks Brian.
Can you give me an example of the "easier to use whole numbers" you'd use in this problem?

[guest612]

i just tried to solve your question and got the same answer. i used fractions and solved it this way, if it helps any:

50% already filled. adding 2/3 gallons will increase it to 70%. therefore 2/3 increases the bucket by 20%.

2/3=0.2x
2/3=1/5x
x=2/3 * 5 = 10/3

[StaceyKoprince]

Please cite the author of the problem - otherwise, it will be deleted. Thanks!