I need help solving this one too

Question

Leilani is a graduate student breeding opihi in a laboratory setting. She found that optimal salt concentration for her experiment to succeed is 4%. If she starts off with 100 liters of 2.5% solution, how much 5.5% solution must she add to create her target salt concentration of 4%?

Answer 1

The formula to solve this question is C1V1 + C2V2 = C3V3 where C = Concentration and V = Volume

 

in this case, C1 = 2.5%, and V1 = 100L

 

to this solution, we need to add x Liters of 5.5% solution to make 100L + x L of 4% solution. To simplify matters, we will use the decimal values of the percentages, namely 0.025, 0.04, and 0.055. The symbol • will equal multiplication.

 

so, 0.025 • 100L + 0.055 • xL = 0.04 • (100L + x)

expanding, we get 2.5L +0.055x = 4L + 0.04x

combining, we get 0.015x = 1.5L

solving, we get x = 100L

 

Proof: 100L •  0.025 + 100L • 0.055 = (100L +100L) • 0.04

2.5L + 5.5L = 8L