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pounds of coffee

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Director
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22 Oct 2006, 13:25
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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.
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22 Oct 2006, 13:35
revise the question i believe it is badly written , thanks

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22 Oct 2006, 13:37
1.2x+1.8y = 18(x+y)

1.5x+2.1y = 21.3(x+y)

if i understand ur question right

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22 Oct 2006, 13:50
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...
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22 Oct 2006, 14:01
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

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22 Oct 2006, 16:40
Does "Valued at \$18.00" mean 18(x+y) or ONLY 18. The question doesn't mention 18 per pound of mixture, does it?

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22 Oct 2006, 18:56
Nope. Not per pound - the \$18.00 refers to the cost of the total mixture.
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22 Oct 2006, 20:39
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;

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22 Oct 2006, 21:11
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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22 Oct 2006, 21:11
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