26kg aluminum magnesium alloy contains 40% aluminum. how much magnesium needs to be added

26kg aluminum magnesium alloy contains 40% aluminum. how much magnesium needs to be added to this alloy to get a new alloy that contains 13% aluminum.

Decision.
1. Find out the mass of aluminum (x) in the total mass of the alloy (26 kg). To do this, let’s make a proportion:
26 kg – 100%,
x kg – 40%.
Let’s find x using the main property of proportion – the “cross” rule:
x = (40% * 26 kg) / 100%.
Numerator and denominator percentages are reduced.
x = (40 * 26 kg) / 100 = (4 * 26) kg / 10 = (2 * 26) kg / 5 = 52 kg / 5 = 10.4 kg (mass of aluminum).
2. In the new alloy, the mass of aluminum will remain the same, but will make up only 13% of the total mass of the new alloy. Find out the mass of the new alloy. To do this, let’s make a proportion:
10.4 kg – 13%,
x kg – 100%.
Let’s find x using the main property of proportion – the “cross” rule:
x = (10.4 kg * 100%) / 13%.
Numerator and denominator percentages are reduced. When multiplying a fraction by 100, the comma in the fraction is moved two positions to the right, since there are two zeros in the number 100.
x = 1040 kg / 13 = 80 kg (the mass of the new alloy).
3. The mass of the new alloy was obtained by adding magnesium. We find out the mass of added magnesium, for this we subtract the mass of the first alloy from the mass of the new alloy:
80 – 26 = 54 (kg).
Answer: to get a new alloy that contains 13% aluminum, you need to add 54 kg of magnesium to the first alloy.