An alloy of gold and silver contains 40 grams of gold. After adding 50 grams of gold to it, a new alloy was obtained

An alloy of gold and silver contains 40 grams of gold. After adding 50 grams of gold to it, a new alloy was obtained in which the gold content increased by 20%. How much silver was in the alloy? Only it is necessary with the use of rational equations.

Let’s take the amount of silver for x, then:

x + 40 is the mass of the first alloy.

40 * 100 / (x + 40) – gold concentration;

x + 40 + 50 = x + 90 is the mass of the resulting alloy;

90 * 100 / (x + 90) – new concentration of gold.

Since the gold content has increased by 20%, we get the equation:

90 * 100 / (x + 90) – 40 * 100 / (x + 40) = 20;

900 * (x + 40) – 400 / (x + 90) = 2 * (x + 40) * (x + 90);

500x = 2x ^ 2 + 180x + 80x + 7200;

x ^ 2 + 130x + 3350 = 0;

x12 = (130 + – √ (16900 – 4 * 1 * 3350)) / 2 = (130 + 60) / 2;

x = 95.