SOLUTION: I'm trying to figure out the formula for this word problem. If I can figure out the formula for mixtures I should be able to do the entire worksheet. Sample Problem: A Chemist

Question 531021: I'm trying to figure out the formula for this word problem. If I can figure out the formula for mixtures I should be able to do the entire worksheet.
Sample Problem: A Chemist has a solution that is 12% acid and another solution that is 42% acid. She wants 10L of solution that is 30% acid. How much of each solution should she mix?
Found 2 solutions by scott8148, oberobic:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
(12%)(x) + (42%)(10 - x) = (30%)(10)
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
With solution problems you need to determine how much 'pure' stuff you have or need.
.
The chemist needs 10 liters of a 30% acid. .3*10 = 3 liters of 'pure' acid in a solvent (likely water).
.
She has 12% acid and 42% acid to mix together.
.
x = liters of 12% acid
y = liters of 42% acid
x+y =10
so
x = 10-y
or
y = 10 - x
.
.12*x + .42*y = .3*10
.
multiply by 100 to eliminate decimals
.
12x + 42y = 30*10
.
substitute for x
.
12(10-y) + 42y = 300
120 -12y + 42y = 300
30y = 180
y = 6
.
Answer: Mix 6 liters of 42% acid and 4 liters of 12% acid.
.
Check the amount of pure acid to be sure this answer is correct.
.42*6 = 2.52
.12*4 = 0.48
2.52 + .48 = 3.0
Correct.
.
Done.
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