Question 1142695: A coffee merchant blended coffee worth 93 cents a pound with coffee worth $1.20 a pound. The mixture of 30 pounds was valued by him at $1.02 a pound. How many pounds of each grade did he use?
Please, if possible, use a model for me.
Found 3 solutions by Theo, greenestamps, josgarithmetic:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = number of pounds of coffee worth 93 cents a pound.
y = number of pounds of coffee worth 120 cents a pound.
30 pound mixture = 102 cents a pound.
your 2 equations that need to be solved simultaneously are:
x + y = 30
93x + 120y = 102 * (x + y)
in the first equation, solve for y to get y = 30 - x.
in the second equation, replace y with 30 - x to get:
93 * x + 120 * (30 - x) = 102 * (x + 30 - x).
simplify to get:
93 * x + 3600 - 120 * x = 102 * x + 3060 - 102 * x.
combine like terms to get:
-27 * x + 3600 = 3060.
subtract 3600 from both sides of the equation to get:
-27 * x = -540.
solve for x to get x = 20.
since x + y = 30, then y has to be equal to 10.
your solution appears to be x = 20 and y = 10
in the first equation, x + y = 30 becomes 20 + 10 = 30 which becomes 30 = 30.
in the second equation, 93 * x + 120 * y = 102 * (x + y) becomes 93 * 20 + 120 * 10 = 102 * 30 which becomes 1860 + 1200 = 3060 which becomes 3060 = 3060.
solution looks good.
solution is that 20 pounds of 93 cents a pound coffee are mixed with 10 pounds of 120 cents a pound coffee to make 30 pounds 102 cents a pound coffee.
93 cents is equal to $.93.
120 cents is equal to $1.20.
102 cents is equal to $1.02.
you divide cents by 100 to get dollars.
you multiply dollars by 100 to get cents.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
I don't know what kind of "model" one would use for this problem....
Here is a solution to your problem using common sense and logical reasoning that is far less work than the formal algebraic solution method shown by the other tutor.
(1) The per-pound cost of the mixture, $1.02, is 1/3 of the way from 93 cents to $1.20. (93 cents to $1.20 is 27 cents; 93 cents to $1.02 is 9 cents; 9/27 = 1/3)
(2) Therefore 1/3 of the mixture must be the more expensive coffee.
ANSWER: 1/3 of 30 pounds, or 10 pounds, of the $1.20 per pound coffee; and 20 pounds of the $0.93 per pound coffee.
Answer by josgarithmetic(39617)  (Show Source):
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