Word Problem!!!!

Question

To keep his baseball team hydrated, Daniel mixes powdered sports drink with cold water. For best taste mix should be 96% water. If Daniel has used 16 scoops of powder and 2 quarts of water, how many gallons of water should he add, given each scoop is 1/4cup?

Answer 1

8 ounces = 1 cup

16 ounces = 1 pint

32 ounces = 1 quart

128 ounces = 1 gallon = 4 quarts

 

16 scoops x (1/4) cup per scoop = 4 cups powder = 1 quart powder

 

96% water means water / (water + powder) = .96

 

let w = quarts of water

 

w / (w + 1) = .96

 

w = .96(w + 1)

w = .96w + .96

.04w = .96

w = 24 quarts = 6 gallons water

 

He already used 2 quarts (1/2 gallon) so he should add 5 1/2 gallons

 

Answer 2

A slightly different approach to this would be to determine, as in the previous answer that he used 1 quart of powder. Then, as stated, this amount will need to constitute 4% of the total mixture. Now, 4% is exactly 1 25th of a whole. Therefore, the powder will be 1 25th of the whole and the water will be the other 24 25th's of the whole. Thus, water will be 24 times the amount of powder, 24 quarts. Which, of course, equals 6 gallons. Since he started with 1/2 a gallon, he will need to add 5 1/2 gallons.  I believe it is also worth noting that, since the mixture is 6 gallons water and 1 quart powder, the total amount of mixture this will produce is 6 1/4 gallons.  This is, 25 quarts total, 24 of water and 1 powder, just as expected.