The first alloy contains 70% copper. The second alloy contains 40%. In what ratio should you take to get

The first alloy contains 70% copper. The second alloy contains 40%. In what ratio should you take to get an alloy containing 50% copper.

Suppose that for the preparation of the required alloy, x kg of a 70% alloy and a kg of a 40% alloy are needed.

This means that the mass of copper in the first alloy will be equal to x * 70: 100 = 0.7 * x kg, and the mass of copper in the second alloy will be equal to y: 100 * 40 = 0.4 * y kg.

The mass of the resulting alloy will be equal to x + y kg, and the mass of copper in it, respectively, (x + y): 100 * 50 = 0.5 * (x + y).

According to the condition of the problem, we compose the equation:

0.7 * x + 0.4 * y = 0.5 * (x + y),

0.7 * x + 0.4 * y = 0.5 * x + 0.5 * y,

0.2 * x = 0.5 * y – 0.4 * y,

0.2 * x = 0.1 * y,

y = 2 * x.

Thus, the second alloy should be taken 2 times more than the first.