How many quarts of water must be added to 7 quarts of a 75% solution of cherry syrup to yield a 30% solution to make frozen slushies? How many quarts of 30% syrup will there be?

Answer 1

75(7) + 0(W) = 30(7+W) = 210+30W

30W = 525 - 210 = 315

W = 315/30 = 63/6 = 21/2 = 10.5 quarts of water

75(7) + 0(10.5) = 30(17.5)

525 = 525

water = 0% solution. 0 is closer to 30 than 75, so you need more water than 75% solution

0 is 30 from 30. 75 is 45 from 30. 45/30 = 3/2 times further away

You need 3/2 or 1.5 time 7 quarts = 10.5 quarts of water

which will make 7+10.5 = 17.5 quarts of 30% syrup