SOLUTION: Three are three type ingots. The first has 20gms gold, 30gms of silver and 40 gms of copper. the second has 30gms of gold, 40gms of silver and 50 gms copper. The third has 40 gms

Question 844459: Three are three type ingots. The first has 20gms gold, 30gms of silver and 40 gms of copper. the second has 30gms of gold, 40gms of silver and 50 gms copper. The third has 40 gms of gold, 50gms silver and 90 gms copper. What weight will be taken from each of the previous ingots to form a new ingot of 34 gms gold, 46 gms silver and 67 gms copper?

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
x = amount from first 90 gram ingot
y = amount from second 120 gram ingot
z = amount from third 180 gram ingot

Account for gold:
Account for silver:
Account for copper:

Simplify the system first, to have lowest-term fraction coefficients:
Gold:
Silver:
Copper:

Simplify the system next multiplying each equation by its lowest common denominator to clear the fractions; using 36 for gold and copper, and using 18 for the silver:
Gold:
Silver:
Copper:

Finish the constant term multiplications:
Gold:
Silver:
Copper:

A software tool for matrices would be best way unless you really wanted to do all the matrix row operations on paper. A useful choice is http://www.math.purdue.edu/~dvb/matrix.html
'
-----------------------------------
RESULT:
(x, y, z) is (45, 48, 54)
MEANING: 45 of number 1 ingots, 48 of number 2 ingots, 54 of number 3 ingot.
-----------------------------------
RELATED QUESTIONS
A jeweler has 30 oz of an alloy consisting of 60 percent gold and 40 percent silver. How... (answered by stanbon)

Owen and Liam have some gold notebooks and some silver notebooks. The number of silver... (answered by josgarithmetic,ikleyn)

A goldsmith has two alloys that are different purities of gold. The first is... (answered by stanbon)

A goldsmith has two alloys that are different purities of gold. The first is... (answered by ptaylor)

A goldsmith has two alloys that are different purities of gold. The first is... (answered by josmiceli)

A goldsmith has two alloys that are different purities of gold. The first is... (answered by Mathtut)

A goldsmith has two alloys that are different purities of gold. The first is... (answered by checkley77)