LINEAR SYSTEM WITH SUBSTITUTION

Question

Fred needs 55 ml of 11% sucrose solution to do his science experiment. He needs to mix a 5% sucrose solution with some 25% sucrose solution to get the 11% solution he wants. How much of each should Fred use? (Include units with your numerical answers.)

Answer 1

25x + 5(55-x) = 11(55)

25x-5x = 6(55)

20x = 6(55

10x = 3(55) = 165

x = 16.5 ml of 25%

55-16.5 = 38.5 ml of 5%

11% is closer to 5 than to 25, so you'd expect more of 5% would be needed than of 25%

11-5 = 6

25-11 = 14

6/14 = 3/7 16.5/38.5 = 33/77 = 3/7. He needs the solutions in a ratio of 3/7 which = 16.5/38.5