Gabe needs ___ liters of the 50​% 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. How many liters of each does he need to make the needed 60 liters of 60% acid solution?

Gabe needs ___ liters of the 50% solution.

Gabs needs ___ liters of the 70% solution.

Answer 1

s represents the amount of 70%

60 - s represents the amount of 50%

 

0.50(60 - s) + 0.70s = 0.60(60)

 

Can you solve for s and answer?

Answer 2

Let x = the number of liters of the 70% solution

Let y = the number of liters of the 50% solution

x + y = 60     x = 60 - y

.70x + .50y = .60(60)     Multiply both sides of the equation by 100 to get rid of the decimal points.

70x + 50y = 60(60) = 3600

70(60 - y) + 50y = 3600

4200 - 70y + 50y = 3600

-20y = -600

y = 30 liters

y = 60 - y = 60 - 30

y = 30 liters