SOLUTION: Delores mixes two types of orange juice, one fortified and one unfortified, to drink with a meal. The fortified juice contains 250 milligrams of vitamin C per cup, and the unfortif
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Question 1189313: Delores mixes two types of orange juice, one fortified and one unfortified, to drink with a meal. The fortified juice contains 250 milligrams of vitamin C per cup, and the unfortified juice contains 150 milligrams of vitamin C per cup. If one cup of Delores's mixture contains 210 milligrams of vitamin C, how much of the fortified orange juice is in one cup of the mixture? Answer by greenestamps(13200) (Show Source):
The objective is to find what fraction of the mixture is the fortified orange juice; then that fraction of one cup is the amount of fortified orange juice in her cup.
A traditional setup for solving the problem might look something like this:
let x = number of cups of fortified orange juice in one cup
then 1-x = number of cups of unfortified orange juice in one cup
Then x cups of fortified orange juice at 250 mg/cup and (1-x) cups of unfortified orange juice at 150 mg/cup yields 1 cup containing 210 mg:
I will leave it to you to find the answer by solving that equation....
An informal solution using logical reasoning is faster and easier.
On a number line, look at the three concentrations of mg/cup of the two ingredients and the mixture -- 150, 210, and 250 -- and observe/calculate that 210 is 60/100 = 3/5 of the way from 150 to 250.
That means 3/5 of the mixture is the fortified orange juice; so her cup of juice contains 3/5 of a cup of the fortified orange juice.
ANSWER: Her cup contains 3/5 of a cup of fortified orange juice
