Answer:
He should combine 1 kg of 30% alloy and 3 kg of 10% alloy.
Step-by-step explanation:
Let x = mass of 30% ally.
Let y = mass of 10% alloy.
He needs 4 kg of alloy, so the first equation, dealing with masses, is
x + y = 4
Now we deal with the amount of gold.
He uses x mass of 30% gold alloy. The amount of gold in that mass is 0.3x.
He uses y mass of 10% gold alloy. The amount of gold in that mass is 0.1y.
The total mass of gold is 0.3x + 0.1y. We are told the told the end alloy is 4 kg of 15% gold alloy. That contains 0.15(4) kg = 0.6 kg of gold.
The second equation is
0.3x + 0.1y = 0.6
Now we put together the two equations as a system of equations.
x + y = 4
0.3x + 0.1y = 0.6
Multiply both sides of the second equation by -10.
-3x - y = -6
Add this equation to the first original equation.
x + y = 4
+ -3x - y = -6
---------------------
-2x = -2
x = 1
Now substitute x = 1 in the first original equation and solve for y.
x + y = 4
x + y = 4
y = 3
Answer: He should combine 1 kg of 30% alloy and 3 kg of 10% alloy.
