Guava extract

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kanha81: Master | Next Rank: 500 Posts; Posts: 431; Joined: Sat Jan 10, 2009 9:32 amFollowed by: 1 member; Thanked: 16 times

by kanha81 » Sat May 30, 2009 11:53 am

Joaquin is inventing a new juice drink. Joaquin combines 15 liters of a juice mix that contains 20% guava extract, with a 20 liter bottle of a different fruit juice mix. If the resulting concoction contains 18% guava extract, what was the original percent of guava extract in the 20-liter bottle of fruit juice mix?

A) 21%
B) 18%
C) 16.5%
D) 15.2%
E) 13.4%

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Source: Beat The GMAT — Problem Solving | Sat May 30, 2009 11:53 am

truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Sat May 30, 2009 12:01 pm

The 15 liters of the juice mix contains 3 liters guava extract. Let x represent the amount of guava extract in the 20 liter bottle of different juice mix.

3+x/35=9/50
150+50x=315
165/50=3.3

Now to find what percent of 20 gives 3.3:

20(x)/100=3.3
x=16.5% C.

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blackarrow: Master | Next Rank: 500 Posts; Posts: 104; Joined: Thu Mar 19, 2009 8:05 pm; Location: Ohio, US; Thanked: 6 times

by blackarrow » Sat May 30, 2009 1:53 pm

Another method thru formula

Basically equating the strength of the mixtures to get the result

15(20%-18%)= 20(18/100-x%)

3/10=(18-100x)/5

ans 16.5

C

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exhilaration: Senior | Next Rank: 100 Posts; Posts: 48; Joined: Thu Dec 04, 2008 12:27 pm; Thanked: 1 times

by exhilaration » Sat May 30, 2009 2:07 pm

truplayer256 wrote:The 15 liters of the juice mix contains 3 liters guava extract. Let x represent the amount of guava extract in the 20 liter bottle of different juice mix.

3+x/35=9/50
150+50x=315
165/50=3.3

Now to find what percent of 20 gives 3.3:

20(x)/100=3.3
x=16.5% C.

Why is it equal to 9/50?

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ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

by ssmiles08 » Sat May 30, 2009 3:24 pm

exhilaration wrote:
truplayer256 wrote:The 15 liters of the juice mix contains 3 liters guava extract. Let x represent the amount of guava extract in the 20 liter bottle of different juice mix.

3+x/35=9/50
150+50x=315
165/50=3.3

Now to find what percent of 20 gives 3.3:

20(x)/100=3.3
x=16.5% C.
Why is it equal to 9/50?

Because 9/50 is 18/100 (18%)simplified.

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