scientist solutions

Question

A  scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 70% salt and Solution B is 95% salt. She wants to obtain 120 ounces of a mixture that is 85% salt. How many ounces of each solution should she use?

Answer 1

A = ounces of A at 70%

B = ounces of B at 95%

 

Do this as a weighted combination of the solutions.

 

(0.70)A + (0.95)B = (0.85)(A + B)

A + B = 120 ounces ⇒ (0.85)(A + B) = 0.85(120) = 102 ounces

 

Solve the system:

 

0.70A + 0.95B = 102

A + B = 120

 

A = 48 ounces of 70% solution

B = 72 ounces of 95% solution