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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

let x be amount of 30% gold and y be amount of 10% gold
to create 4 kg of an alloy, means
x%2By=4...solve for x
x=4-y.........eq.1
0.30x%2B0.10y=0.15%2A4........eq.2
substitute x from eq.1
0.30%284-y%29%2B0.10y=0.6.......solve for y
1.2-0.30y%2B0.10y=0.6
-0.20y=0.6-1.2
-0.20y=-0.6
y=-0.6%2F-0.20
y=3
go to
x=4-y.........eq.1, substitute y
x=4-3
x=1
to create 4 kg of an alloy containing 15% gold, the jeweler should combine 1kg of 30% gold and 3kg of 10% gold


Answer by VFBundy(438) About Me  (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