A scientist has two 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
20%
salt and Solution B is
70%
salt. She wants to obtain
160
ounces of a mixture that is
55%
salt. How many ounces of each solution should she use?

Answer 1

solution A            solution B           Product 

 

20% salt              70% salt            55% salt

   x                           y                  160 oz.

 

 

Let x = amount of solution A 

     y = amount of solution B 

 

 

0.2x + 0.7y = 0.55 (160)

0.2x + 0.7y = 88    (equation 1)

 

 

0.2x + 0.7y = 88

    x +      y = 160  (equation 2)

_________________

 

Use elimination method. Multiply eq. 2 by -0.2 to eliminate x.

 

0.2x + 0.7y = 88                      0.2x + 0.7y = 88 
     x +     y = 160 (-0.2) --->   -0.2x -  0.2y = -32
_________________                ________________

 

                                                         0.5y = 56

                                                       y = 112 oz.

 

Solve for x. 

 

x + y = 160

x + 112 = 160

x = 160 - 112

 

x = 48 oz