SOLUTION: pure acid is to be added to a 10% acid solution to obtain 42 L of a 40% acid solution. What amounts of each should be used? blank L of pure acid solution and blank L of 10% acid

Question 534337: pure acid is to be added to a 10% acid solution to obtain 42 L of a 40% acid solution. What amounts of each should be used?
blank L of pure acid solution and blank L of 10% acid solution
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
x = amount 10% acid
y = amount of pure acid
.
x+y = 42 liters
x = 42-y
y = 42-x
.
The desired solution is 42 liters of a 40% solution. It will contain 42*.40 liters of pure acid.
42*.4 = 16.8 liters of pure acid and 25.2 liters of solvent (probably water).
.
10%*x + 100%*y = 40%*42
.1*x + y = 16.8
.
multiply both sides by 10 to eliminate the decimals
.
x + 10y = 168
.
substitute for x = 42-y
.
42-y +10y = 168
9y = 126
y = 126/9 = 42/3 = 14
.
x = 42-14
x = 28
.
Check how much 'pure' acid is in the solution.
28 * 10% acid = 2.8 liters of pure acid
13 * 100% acid = 14 liters of pure acid
2.8 + 14 = 16.8 liters of pure acid in the 42 liters of solution
.
Answer: Mix 14 liters of pure acid and 28 liters 10% acid to make 42 liters of 40% acid.
.
Done.

RELATED QUESTIONS
Pure acid is to be added to a 10% acid solution to obtain 90 L of a 20% acid solution.... (answered by josgarithmetic)

Pure acid is to be added to a 10% acid solution to obtain 90 L of a 20% acid solution.... (answered by Alan3354)

Pure acid is to be added to a 10% acid solution to obtain 81 L of a 20% acid solutions.... (answered by ankor@dixie-net.com)

pure acid is to be added to a 10% acid solution to obtain 90L of 42% solution what... (answered by addingup)

pure acid is to be added to a 20% acid solution to obtain 40L of a 40% acid solution.... (answered by josgarithmetic)

pure acid is to be added to a 10% solution to obtain 45L of a 40% acid solution. What... (answered by josmiceli)

Pure acid is to be added to a 10% acid solution to obtain 54L of a 20% acid solution.... (answered by longjonsilver)

Pure Acid is to be added to a 10% acid solution to obtain 27 litters of 20% acid... (answered by robertb)

Pure acid is to be added to a 10% acid solution to obtain 126 L of a 20% acid solution.... (answered by jsmallt9)