How many liters of each does he need to make the needed 60 liters of 60% acid solution?

Question

Gabe Amodeo, a nuclear physicist, needs 60 liters of a 60% acid solution. He currently has a 50% solution and a 70% solution.

Answer 1

Let x = the amount of 50% solution used

Let y = the amount of 70% solution used

 

Since he needs 60 liters total

x + y = 60

 

Since he needs 60% acid solution

0.5x + 0.7y = 60 * 0.6

 

Now we you have two equations, solve the system.

 

Multiply both sides of the second equation by 2

x + 1.4 y = 72

 

Subtract the new equation by the first equation

0.4 y = 12

 

Solve for y

 

y = 30

 

Solve for x

 

x = 30

 

He needs 30 L of 50% acid solution and 30 L of 70% acid solution