The alloy consists of tin and lead with a tin content of 60%, another alloy contains the same metals with a tin content of 40%.

The alloy consists of tin and lead with a tin content of 60%, another alloy contains the same metals with a tin content of 40%. How many grams of each should be taken to obtain 600 g of an alloy containing 45% tin?

Let’s introduce variables. Let m be the mass of the first alloy, n – the mass of the second alloy.

The mass of tin in the first alloy is 0.6 * m, the mass of tin in the second alloy is 0.4 * n.

Based on the conditions of the problem and the mass and concentration of the substance in the new alloy, we will compose and solve a system of two equations:

m + n = 600;

0.6 * m + 0.4 * n = 270;

m = 600-n;

Substitute the expression into the second equation:

0.6 * (600 – n) + 0.4 * n = 270;

360 – 0.6 * n + 0.4 * n = 270;

0.2 * n = 90;

n = 450;

m = 150;

Answer: The weights of the solutions are 450 g and 150 g.