How many liters of 32% acid and how many liters of 22% acid must be mixed together to obtain 10 liters of a mixture that is 25% acid?

Question

Please show work to help me better understand

Answer 1

Let x = the amount of 32% acid, and let y = the amount of 22% acid

 

x + y = 10  (the total amount of acid in liters)

 

Also:

 

If we change the percents to decimals:

 

x(0.32) + y(0.22) = 10(0.25)

 

Since y = 10 - x when we solve form, we can use the Substitution Method to solve for x:

 

x(0.32) + (10 - x)(0.22) = 2.5

 

Multiply both sides by 100 to eliminate the decimals

 

32x + (10 - x)(22) = 250

 

32x+ 220 - 22x = 250

 

10x + 220 = 250

 

10x = 30

 

x = 3 L of 32% acid

 

y = 10 - x = 10 - 3 = 7 L of 22% acid