how to find the solution?

Question

etch clean graphics uses one cleanser that s 25% acid and a second that is 50% acid. how many liters of each should be mixed to get 30L of a solution that is 40% acid?

Answer 1

graphics uses one cleanser that s 25% acid and a second that is 50% acid. how many liters of each should be mixed to get 30L of a solution that is 40% acid?

30 L of 40% cleanser will contain 30 * 40% = 12 L acid.

Let there be V1 L of cleanser at 25% giving V1 * 25% = V1/4 L of acid

Let there be V2 L of cleanser at 50% giving V2 * 50% = V2/2 L of acid

Therefore V1/4 + V2/2 = 12 --------- (1)

And V1 + V2 = 30   -------------------- (2)

Multiplying (1) by 4,

V1 + 2V2 = 48  -------------------------- (3)

V1 + V2 = 30   --------------------------- (2)

Subtracting (2) from (3),

V2 = 18. therefore, V1 = 30 - 18 = 12

Answer: Mix together 12 L of the 25% cleanser and 18 L of the 50% cleanser to get 30 L of 40% cleanser