Solving a percent mixture problem using a system of linear equations

Question

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is
45%
salt and Solution B is
70%
salt. She wants to obtain
170
ounces of a mixture that is
55%
salt. How many ounces of each solution should she use?

Answer 1

let the mass of A required be a

 

let the mass of B required be b

 

final mixture is 170 * 55% = 93.5 grams of salt

 

       a +       b = 170       (1)       (total mass of solution)

 

0.45a + 0.70b =   93.5     (2)       (proportion of each solution required in final salt solution)

 

multiply (1) by -0.45 

 

-0.45a - 0.45b =  -76.5       (3)

 

add (2) to (3)  ; 0.25b = 17

 

therefore b = 17/0.25 = 68

 

from (1) a = 170 - 68 = 102

 

Therefore 68 grams of B and 102 grams of A are required for the final solution mixture