How much 20% and 40% copper alloy should be mixed to yield 500 kilograms of 25% copper alloy
To solve this problem, we need to use the concept of mixtures. Let's break it down step by step:
Step 1: Assign variables
Let's assume that the amount of 20% copper alloy to be mixed is x kilograms, and the amount of 40% copper alloy to be mixed is y kilograms.
Step 2: Set up equations
The equation representing the total amount of the mixture is:
x + y = 500
The equation representing the amount of copper in the mixture is calculated by multiplying the percentage of copper in each alloy by its respective weight:
0.20x + 0.40y = 0.25 * 500
Step 3: Solve the equations
We have a system of two equations with two unknowns. We can solve this system of equations using various methods such as substitution, elimination, or matrix equations.
For simplicity, let's solve it using substitution:
From the first equation, we can express x in terms of y, as x = 500 - y. Substituting this value into the second equation gives us:
0.20(500 - y) + 0.40y = 0.25 * 500
Simplifying the equation:
100 - 0.20y + 0.40y = 125
0.20y = 25
y = 125
Substituting the value of y back into the first equation:
x + 125 = 500
x = 375
So, 375 kilograms of 20% copper alloy and 125 kilograms of 40% copper alloy should be mixed to yield 500 kilograms of 25% copper alloy.
box 1
x kg
.2x copper
.8 x whatever
box 2
y kg
.4 y copper
.6 y whatever
box 3
x+y kg = 500
.25*500 = 125 kg copper
375 kg whatever
so
125 = .2 x + .4 y
500 = x + y
take it from there