SOLUTION: A goldsmith combined an alloy that costs $4.30 per ounce with an alloy that costs $1.80 per ounce. How many ounces of each were used to make a mixture of 200 oz costing $2.35 per o

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A goldsmith combined an alloy that costs $4.30 per ounce with an alloy that costs $1.80 per ounce. How many ounces of each were used to make a mixture of 200 oz costing $2.35 per o      Log On


   

Question 1175417: A goldsmith combined an alloy that costs $4.30 per ounce with an alloy that costs $1.80 per ounce. How many ounces of each were used to make a mixture of 200 oz costing $2.35 per ounce?
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Ounces of $4.30 alloy = x
Ounces of $1.80 alloy = y

Make two equations:

x + y = 200
4.30x + 1.80y = 200(2.35)

Simplify second equation:

4.30x + 1.80y = 470

Here are your two equations:

x + y = 200
4.30x + 1.80y = 470

Multiply first equation by -1.80:

-1.80x - 1.80y = -360

Here are your two equations:

-1.80x - 1.80y = -360
4.30x + 1.80y = 470

Add both equations together:

2.50x = 110

Solve for x:

x = 44

Plug x = 44 into the original first equation to find y:

x + y = 200

44 + y = 200

y = 156

Ounces of $4.30 alloy = x = 44
Ounces of $1.80 alloy = y = 156