Question 1189313
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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.<br>
A traditional setup for solving the problem might look something like this:<br>
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<br>
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:<br>
{{{x(250)+(1-x)(150)=1(210)}}}<br>
I will leave it to you to find the answer by solving that equation....<br>
An informal solution using logical reasoning is faster and easier.<br>
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.<br>
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.<br>
ANSWER: Her cup contains 3/5 of a cup of fortified orange juice<br>