A chemist needs 22 liters of a 14% acid solution. He has a 10% solution and a 20% solution available to form the mixture. How much of each should be used to form the 14% solution?
I'm having a really hard time forming an equation for this. I've tried creating a system for elimination, but that doesn't work--nor does substitution.
He is supposed to need 2 liters, not 22! Sorry for the typo
To solve this problem, let's introduce two variables:
Let's say x represents the amount of the 10% acid solution needed and y represents the amount of the 20% acid solution needed.
Now, we can create two equations based on the given information:
1. Equation for the total volume of the mixture:
x + y = 22 (since the chemist needs a total of 22 liters of the final solution)
2. Equation for the acid concentration:
0.10x + 0.20y = 0.14(22) (since the acid concentration of the final solution should be 14%)
Let's solve this system of equations using the substitution method:
From equation 1, we can express x in terms of y:
x = 22 - y
Substitute this expression for x in equation 2:
0.10(22 - y) + 0.20y = 0.14(22)
2.2 - 0.1y + 0.20y = 3.08
0.10y = 3.08 - 2.2
0.10y = 0.88
y = 0.88 / 0.10
y = 8.8
Now, substitute the value of y back into equation 1 to find x:
x + 8.8 = 22
x = 22 - 8.8
x = 13.2
Therefore, the chemist should use 13.2 liters of the 10% solution and 8.8 liters of the 20% solution to form the 22 liters of the 14% solution.