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# pounds of coffee

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Director
Joined: 11 Sep 2006
Posts: 514
Followers: 2

Kudos [?]: 35 [0], given: 0

pounds of coffee [#permalink]  22 Oct 2006, 12:25
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A mixture of coffee worth $1.20 a pound and of coffee worth$1.80 a pound is valued at $18.00. If the price per pound of each grade is increased$.30, the new value of the mixture would be $21.30. Find the number of pounds of coffee for each grade. Guys, this problem is from an algebra text, so no multiple choice answers...but I've seen something like it before on GMATprep. Can't seem to wrap my head around this one...thanks for your help. _________________ ...there ain't no such thing as a free lunch...  Kaplan GMAT Prep Discount Codes Knewton GMAT Discount Codes GMAT Pill GMAT Discount Codes SVP Joined: 05 Jul 2006 Posts: 1516 Followers: 5 Kudos [?]: 124 [0], given: 39 [#permalink] 22 Oct 2006, 12:35 revise the question i believe it is badly written , thanks SVP Joined: 05 Jul 2006 Posts: 1516 Followers: 5 Kudos [?]: 124 [0], given: 39 [#permalink] 22 Oct 2006, 12:37 1.2x+1.8y = 18(x+y) 1.5x+2.1y = 21.3(x+y) if i understand ur question right Director Joined: 11 Sep 2006 Posts: 514 Followers: 2 Kudos [?]: 35 [0], given: 0 [#permalink] 22 Oct 2006, 12:50 Yezz - I actually wrote down the question exactly as presented in the text I had...the answers were given as 3 pounds at$1.20 and 8 pounds at $1.80 - what I'm wondering is if there is an easier way than to combine equations? That's where I got bogged down... _________________ ...there ain't no such thing as a free lunch... SVP Joined: 01 May 2006 Posts: 1798 Followers: 8 Kudos [?]: 102 [0], given: 0 [#permalink] 22 Oct 2006, 13:01 uphillclimb wrote: Yezz - I actually wrote down the question exactly as presented in the text I had...the answers were given as 3 pounds at$1.20 and 8 pounds at $1.80 - what I'm wondering is if there is an easier way than to combine equations? That's where I got bogged down... To me, there is no other way than to combine the equations ... And I could be more or less easy depending on the way to do so Manager Joined: 01 Feb 2006 Posts: 78 Location: New York Followers: 1 Kudos [?]: 0 [0], given: 0 Query [#permalink] 22 Oct 2006, 15:40 Does "Valued at$18.00" mean 18(x+y) or ONLY 18. The question doesn't mention 18 per pound of mixture, does it?
Director
Joined: 11 Sep 2006
Posts: 514
Followers: 2

Kudos [?]: 35 [0], given: 0

Nope. Not per pound - the \$18.00 refers to the cost of the total mixture.
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Senior Manager
Joined: 14 Aug 2006
Posts: 365
Followers: 1

Kudos [?]: 5 [0], given: 0

1.20x + 1.80 y = 18.00
Increased by .30

1.50x + 2.10y = 21.30

These are the two eqs.

2x + 3y = 30
5x + 7y = 71

=>

10x + 15y = 150
10x + 14y = 142
y = 8; x = 3;
Intern
Joined: 01 Oct 2006
Posts: 7
Followers: 0

Kudos [?]: 0 [0], given: 0

This is how I solved it:

1.2x + 1.8y = 18
1.5x + 2.1y = 21.3

subtract the first equation from the second equation, you get
.3x + .3y = 3.3 or x + y = 11

substitute the above value back to either one equation and solve for x:
1.2x + 1.8 (11 - x) = 18
1.2x + 19.8 - 1.8x = 18
.6x = 1.8
x = 3
y = 11 - 3 = 8
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