SOLUTION: A metal alloy is 30% nickel. Another metal ally is 70% nickel. The two alloys are mixed to produce 20kg of a metal alloy that is 48% nickel. How much of each metal alloy is used.

Question 980590: A metal alloy is 30% nickel. Another metal ally is 70% nickel. The two alloys are mixed to produce 20kg of a metal alloy that is 48% nickel. How much of each metal alloy is used.
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52816) (Show Source): You can put this solution on YOUR website!

Let x be the mass of the first alloy (first piece) in kilograms, and let y be the mass of the second alloy (second piece) in kilograms.

Then you have first equation

x + y = 20.

The first alloy contains 0.3*x kilograms of nickel, and the second alloy contains 0.7*y kilograms of nickel. Therefore the mix contains 0.3*x + 0.7*y kilograms of nickel.

It gives you the second equation

0.3*x + 0.7*y = 0.48*20 = 9.6.

So, you have the system of two linear equations in two unknowns

.

Solve yourself this system.

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = kg of 30% alloy needed
Let = kg of 70% alloy needed
kg of nickel in 48% alloy
---------------------
(1)
(2)
------------------------------
(2)
(2)
Multiply both sides of (1) by and
subtract (1) from (2)
(2)
(1)
-----------------------

and
(1)
(1)
-----------------
11 kg of 30% alloy is needed
9 kg of 70% alloy is needed
---------------------------
check:
(2)
(2)
(2)
(2)
(2)
OK
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