Problema Solution
Jane's rum punch recipe calls for 1.5 times as much 100 proof jamaican rum as 80 proof puerto rican rum, both added to hawaiian punch (which has no alcohol). from past experience, Jane knows that if John drinks more than 2ounces of alcohol, he'll take too much time saying grace. yet, John always has an 8 ounce glass of rum punch. in the world of alcoholic beverages, every 2 proof is 1% alcohol. if Jane uses 96 ounces of hawaiian punch, what is the maximum number of ounces of jamaican rum she can use to keep uncle john from taking too much time to say grace? (round to nearest whole number)
Answer provided by our tutors
In the United States, alcoholic proof is defined as twice the percentage of alcohol by volume
100 proof jamaican rum is 100/2 = 50% jamaican rum
80 proof puertorican rum is 80/2 = 40% puertorican rum
let
x = oz of puertorican rum used then
1.5x = oz of jamaican rum used
1.5x oz(50%) +x oz(40%) +96 oz(0%)=(96+2.5x)(1%)
1.5x*0.5 + x*0.4 + 96*0 = (96 + 2.5x)*0.01
by solving the equation we find
x=0.8565 oz of Puerto Rican Rum
1.5x = 1.2848 oz = 1 oz of Jamaican rum
click here to see the step by step solution of the equation
he maximum number of ounces of jamaican rum that Jene can use is 1 oz.