SOLUTION: Here is my problem:
Define the variables and write and solve a system of equations:
A metal alloy is a metal made by blending 2 or more types of metals. A jeweler has supplies
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Question 1156694: Here is my problem:
Define the variables and write and solve a system of equations:
A metal alloy is a metal made by blending 2 or more types of metals. A jeweler has supplies of two metal alloys. One alloy is 30% gold and the other is 10% gold. How much of each alloy should the jeweler combine to create 4kg of an alloy containing 15% gold?
Define variables:
Equations:
Thank you
Found 2 solutions by MathLover1, VFBundy:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
let be amount of % gold and be amount of % gold
to create kg of an alloy, means
...solve for
.........eq.1
........eq.2
substitute from eq.1
.......solve for
go to
.........eq.1, substitute
to create kg of an alloy containing % gold, the jeweler should combine of % gold and of % gold
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
Kg of 30% gold alloy = x
Kg of 10% gold alloy = y
x + y = 4
0.30x + 0.10y = 0.15(4)
x + y = 4
0.30x + 0.10y = 0.60
-0.10(x + y) = -0.10(4)
0.30x + 0.10y = 0.60
-0.10x - 0.10y = -0.40
0.30x + 0.10y = 0.60
0.20x = 0.20
x = 1
If x =1, and x + y = 4, then that means y = 3.
Kg of 30% gold alloy = x = 1
Kg of 10% gold alloy = y = 3
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