Question

# 48 kg of 30% sulfuric acid in a mixture of 10% and 40% sulfuric acid arose. How many kilograms were each of the original solutions?

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## Answer to a math question 48 kg of 30% sulfuric acid in a mixture of 10% and 40% sulfuric acid arose. How many kilograms were each of the original solutions?

Jett
4.7
Let's assume that x kg of 10% sulfuric acid solution is mixed with y kg of 40% sulfuric acid solution to obtain 48 kg of the final mixture.

Step 1: Write the equation based on the amount of sulfuric acid in the mixture:
0.1x + 0.4y = 0.3$48$

Step 2: Simplify the equation:
0.1x + 0.4y = 14.4

Step 3: Use the fact that the total mixture is 48 kg:
x + y = 48

Step 4: Solve the system of equations.
First, multiply the first equation by 10 to eliminate decimals:
10$0.1x + 0.4y$ = 10$14.4$
x + 4y = 144

Now, subtract the second equation from the first equation:
x + 4y - x - y = 144 - 48
3y = 96

Divide both sides of the equation by 3:
y = \frac{96}{3}
y = 32

Substitute the value of y into the second equation to find x:
x + 32 = 48
x = 48 - 32
x = 16

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