SOLUTION: .............Lead....Zink....Copper Alloy A..40%...30%...30% Alloy B..20%...30%...50% Alloy C..........10%...90% How many grams of each alloys A, B, and C must be mixed to ge

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Question 353765: .............Lead....Zink....Copper
Alloy A..40%...30%...30%
Alloy B..20%...30%...50%
Alloy C..........10%...90%
How many grams of each alloys A, B, and C must be mixed to get 325g of an alloy that is 15.2% lead, 37.2% zink, and 47.6% copper?
I've tried this using the Matrix, and the inverse Matrix, and keep coming up with negitives on some alloys.
Thanks for your help.
Neil
Found 2 solutions by Fombitz, scott8148:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let X be the amount of alloy A, Y alloy B, Z alloy C.
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Lead:40X%2B20Y%2B0Z=15.2%28X%2BY%2BZ%29=15.2%28325%29=4940
Zinc:30X%2B30Y%2B10Z=37.2%28325%29=12090
Copper:30X%2B50Y%2B90Z=47.6%28325%29=15470
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Using matrix inversion,

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%28matrix%283%2C1%2CX%2CY%2CZ%29%29=%28matrix%283%2C1%2C-195%2C637%2C-117%29%29
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I get the same answer.
Something is up with the problem setup.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
(40)(A) + (20)(B) + (0)(C) = (15.2)(325)

(30)(A) + (30)(B) + (10)(C) = (37.2)(325)

(30)(A) + (50)(B) + (90)(C) = (47.6)(325)