At the local retirement home, a popular drink is CranOrange craze, a mixture of
ID: 3116709 • Letter: A
Question
At the local retirement home, a popular drink is CranOrange craze, a mixture of cranberry juice and orange juice. Betty likes her mixture to be 30% cranberry juice and 70% orange juice. Her husband Don likes his mixture to be 60% cranberry juice and 40% orange juice. Ethel is very picky, however, and she likes her mixture to be 53% cranberry and 47% orange. One day, Betty and Don visit Ethel’s apartment. Betty brings 6 quarts of her mixture and Don brings 4 quarts of his mixture. Ethel decides to mix them together. She then wants to add either pure cranberry juice or pure orange juice to make the resulting mixture 53% cranberry and 47% orange. How much and which kind of juice does she need to add? Using an algebraic equation?
Explanation / Answer
6 quarts of (30-70) juice have -
cranberry = 6*30% = 1.8
orange = 6*70% = 4.2
4 quarts of (60-40) juice have -
cranberry = 4*60% = 2.4
orange = 4*40% = 1.6
total cranberry = 1.8+2.4 = 4.2
total orange = 4.2+1.6 = 5.8
this mixture is 42%-58%.
to make it 53%-47%, clearly she has to add more of cranberry
47% is equal to 5.8
so 53% is equal to 5.8*53% /47% = 6.54
so additional 6.54-4.20 = 2.34 quarts of craneberry juice has to be added.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.