Question

В сплаве меди и цинка содержится 20 кг цинка. Когда к сплаву добавили 10 кг цинка, его процентное содержание увеличилось на 10%. Найдите первоначальную массу сплава, если она меньше 50 кг.

Answer 1

Пусть масса сплава х кг, тогда первоначальное % содержание меди 20/х*100 %. 
После добавления меди масса стала ,
20+10=30 кг меди, а масса сплава (х+10)
30/(х+10)*100-20/х*100=10
1000(3/(х+10)-2/х))=10
100((3х-2х-20)/(х*(х+10))=1
100(х-20)=х(х+10)
х²+10х-100х+2000=0
х²-90х+2000=0
D=90²-4*2000=8100-8000=100=10²
x₁=(90+10)/2=50 кг
x₂=(90-10)/2=40 кг
Т.е. масса сплава или 40 кг или 50 кг.

Answer 2

Problem Analysis

We are given that there is a copper-zinc alloy containing 20 kg of zinc. When 10 kg of zinc is added to the alloy, the percentage of zinc in the alloy increases by 10%. We need to find the initial mass of the alloy if it is less than 50 kg.

Solution

Let's assume the initial mass of the alloy is x kg.

According to the problem, the initial mass of zinc in the alloy is 20 kg. When 10 kg of zinc is added, the percentage of zinc in the alloy increases by 10%.

To find the new percentage of zinc in the alloy, we can use the formula:

New percentage of zinc = (mass of zinc / total mass of alloy) * 100

Let's calculate the new percentage of zinc in the alloy:

New percentage of zinc = ((20 + 10) / (x + 10)) * 100

We know that the new percentage of zinc is 10% more than the initial percentage of zinc.

So we can write the equation:

((20 + 10) / (x + 10)) * 100 = (20 / x) * 100 + 10

Simplifying the equation:

(30 / (x + 10)) * 100 = (20 / x) * 100 + 10

Cancelling out the common factors:

30 / (x + 10) = 20 / x + 10

Cross-multiplying:

30x = 20(x + 10) + 10(x + 10)

Simplifying:

30x = 20x + 200 + 10x + 100

30x = 30x + 300

Subtracting 30x from both sides:

0 = 300

This equation has no solution, which means there is no initial mass of the alloy that satisfies the given conditions. Therefore, the problem is not solvable.

Conclusion

The initial mass of the alloy cannot be determined because the given conditions lead to an unsolvable equation.