How many ounces of each solution should she use?

Question

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65%

 salt and Solution B is 95%

salt. She wants to obtain 90

 ounces of a mixture that is 85%

 salt. How many ounces of each solution should she use? 

Answer 1

85 is within 10 of 95 but within 30 of 65. 95 is 3 times closer to 85 than to 65 3 times as much 95% is needed.

.95(x) + .65(90-x) = 90(.85)

.95x -.65x = 80(.85-.65) = 90(.20)= 18

.3x = 18

x= 60 ounces of 95% the B solution

80-x = 20 ounces of 65% the A solution

three times as much of 95% as 65% 60=3(20)

Answer 2

(x ounces )Solution A + (y ounces) Solution B = (x + y ounces) Solution C

We know that x + y = 90 ounces. 90 ounces of Mixture C

x (0.65) + y (0.95) = (x + y) (0.85)

0.65x + 0.95y = 0.85x + 0.85y

0.1y = 0.2x

y = 2x

Substitute into the equation x + y = 90 ounces

x + (2x) = 90 ounces

x = 30 ounces

y = 2(30 ounces) = 60 ounces

She should use 30 ounces of Solution A and 60 ounces of Solution B.