There are two alloys of gold and silver. The first alloy contains 32% gold, the second 46% gold.

There are two alloys of gold and silver. The first alloy contains 32% gold, the second 46% gold. What is the ratio of these two alloys to get an alloy containing 42% gold?

Suppose it took x of the first alloy to prepare the required alloy. It will contain gold:

x * 32: 100 = 0.32 * x.

Suppose that the second alloy was required for y, the amount of gold in it will be equal to:

y * 46: 100 = 0.46 * y.

Hence, according to the condition of the problem, we can compose the following equation:

0.32 * x + 0.46 * y = (x + y) * 42: 100,

0.32 * x + 0.46 * y = 0.42 * x + 0.42 * y,

0.46 * y – 0.42 * y = 0.42 * x – 0.32 * x,

0.04 * y = 0.1 * x,

x / y = 0.04 / 0.1,

x / y = 2/5.

This means that the ratio of the first and second alloys is 2/5.