math homework

Question

this is a question in my algebra book.How many cubic centimeters of a 25% antibiotic solution should be added to 10 cubic centimeters of a 60% antibiotic solution in order to get a 30% antibiotic solution?

 

calculate: 

Answer 1

the formula to solve this problem is C1V1 + C2V2 = C3V3 where C = concentration as a decimal, and V = volume

 

let x = volume of 25% solution needed to dilute the 10cc of 60% solution to obtain 10cc + x of 30% solution

 

our equation becomes 10•0.6 + 0.25x = (10 + x)•0.3

we get 6cc +0.25x = 3cc + 0.3x

combining, we get 3cc = 0.05x

solving, x = 60cc

 

Proof: 10cc•0.6 + 60cc•0.25 = (10cc + 60cc)•0.3

6cc + 15cc = 21cc

Answer 2

c represents cc's added.

 

0.25c + 0.6(10) = 0.3(10 + c)

0.25c + 6 = 3 + 0.3c

0.25c + 3 = 0.3c

3 = 0.05c

60 = c