Two alloys were combined with a copper content of 40% and 60% to give an alloy containing 45% copper

Two alloys were combined with a copper content of 40% and 60% to give an alloy containing 45% copper. Find the ratio of the mass of the 40% copper alloy to the mass of the 60% copper alloy.

Let’s introduce variables:

p is the mass of the first alloy;

v is the mass of the second alloy.

The first alloy contains forty percent copper. The mass of the alloy is p kilograms. Let’s find the mass of copper in the first alloy.

p * 40% = 0.4p (kg)

The second alloy contains sixty percent copper. The mass of the alloy is v kilograms. Let’s find the mass of copper in the second alloy.

v * 60% = 0.6v (kg)

The total mass of copper in both alloys is 0.4p + 0.6v kilograms.

The two alloys are combined. The mass of the resulting alloy is p + v kilograms.

According to the condition of the problem, the resulting alloy contains forty-five percent copper. Let’s find out how many kilograms of copper are in the resulting alloy.

0.45 * (p + v) = 0.45p + 0.45v (kg)

So, in the resulting alloy, 0.45p + 0.45v kilograms of copper.

And we previously found out that the total mass of copper in the two alloys is 0.4p + 0.6v kilograms. This means that the resulting alloy contains 0.4p + 0.6v kilograms of copper. We can make an equation.

0.45p + 0.45v = 0.4p + 0.6v.

Move 0.4p from the right side of the equation to the left side of the equation.

0.45p + 0.45v – 0.4p = 0.6v;

0.05p + 0.45v = 0.6v.

Move 0.45v from the left side of the equation to the right side of the equation.

0.05p = 0.6v – 0.45v;

0.05p = 0.15v.

p = 0.15v / 0.05;

p = 3v.

Divide both sides of the equation by v. We can do this because we know that v ≠ 0.

p / v = 3.

We found that the mass of the first alloy is related to the mass of the second alloy as three to one.

The answer is three to one.