SOLUTION: Mr. Lyons wishes to make a mixture of 12 pounds of tea worth $1.20 per pound by mixing tea worth $1.00 per pound with tea worth $1.30 per pound. What part of the mixture will be ma

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Question 1162586: Mr. Lyons wishes to make a mixture of 12 pounds of tea worth $1.20 per pound by mixing tea worth $1.00 per pound with tea worth $1.30 per pound. What part of the mixture will be made up of the less expensive grade?
Found 3 solutions by ankor@dixie-net.com, greenestamps, josgarithmetic:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
Mr. Lyons wishes to make a mixture of 12 pounds of tea worth $1.20 per pound by mixing tea worth $1.00 per pound with tea worth $1.30 per pound.
What part of the mixture will be made up of the less expensive grade?
:
let x = amt of $1 tea required
then
(12-x ) = $1.30 tea required
:
1x + 1.3(12-x) = 1.2(12)
x + 15.6 - 1.3x = 14.4
-.3x = 14.4 - 15.6
-.3x = -1.2
x = -1.2/-.3
x = +4 pounds of the cheap stuff
:
:
Check: (12 - 4 = 8 lb of $1.30 tea)
1(4) + 1.3(8) = 1.2(12)
4 + 10.4 = 14.4

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

You should understand how to solve this kind of problem by the standard algebraic method, as shown by the other tutor.

However, if a formal algebraic solution is not required, look how easy it is to solve this problem:

$1.20 is 2/3 of the way from $1.00 to $1.30.
Therefore, 2/3 of the mixture is the tea worth $1.30 per pound.

ANSWER: 2/3 of the 12 pounds, or 8 pounds, is the tea worth $1.30 per pound; the other 4 pounds is the tea worth $1.00 per pound.

CHECK:
8(1.30)+4(1.00) = 10.40+4.00 = 14.40
12(1.20) = 14.40

You can use that method to solve ANY two-part mixture problem....

Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!
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make a mixture of 12 pounds of tea worth $1.20 per pound by mixing tea worth $1.00 per pound with tea worth $1.30 per pound. What part of the mixture will be made up of the less expensive grade?
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make a mixture of P pounds of tea worth $T per pound by mixing tea worth $L per pound with tea worth $H per pound. What part of the mixture will be made up of the less expensive grade, the $L per pound?
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x of the less expensive grade
P-x of the other grade

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and you know that in this form, numerator and denominator of the fraction are both negative, so simply

The question asked for essentially .

Substitute your given values.