Juice Mixup 1
(page 166)

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A couple of Ohioans sent in this solution (January 2010):

Mr. Erickson,

We are Taylor D. and Dennis G. from a middle school in central Ohio. We are in 6th and 8th grade, respectively, and we think we have come up with a solution for Juice Mixup 1.

First we learned that Denny made orange juice with one can of concentrate and four cans of water to make a 20% solution (4:1). Then, we were asked to find three key pieces of information:
a. What was the percent of Isabel's orange juice solution?
b. What was the percent of the regular (correct) orange juice solution?
c. How much of Isabel's plus Denny's solutions are needed to mix together to get orange juice in the correct proportion?

Based on the clues, we found that Isabel mixed two cans of water with every can of orange juice concentrate for a 50% solution (2:1). We then logically assumed that the solution for the regular (correctly tasting) orange juice should be 30% or a 3:1.

In order to make a 3:1 for the regular orange juice, we must take one fifth (1/5) of Isabel's solution and all of Denny's solution to make the orange juice. For example:

10% solution of Isabel's + 20% solution of Denny's = 30% correct tasting solution

Which means we could theoretically take one gallon of Isabel's orange juice plus 4 gallons of Denny's orange juice to get 5 gallons of orange juice that tastes correct.


eeps comments:

This is a very interesting solution. Readers, wht do you think?

Working with ratios can be confusing. Here is an example: They say that Denny has a 20% solution because his orange juice is 4:1. Why is 4:1 a 20% solution? Draw a picture of what he did, maybe like this:

[juice] [water] [water] [water] [water].

That's 4:1, so that means that one in FIVE is juice. And that's 20%.

But later, they say that a 2:1 solution is 50%. Is that correct? Wouldn't that be

[juice] [water] [water] ?

And that looks to me like 33%...Check with the original problem to see what's up!

Then, see the boldface paragraphs at the bottom? What they say may be correct, or not (I'll never tell!) but it's not obvious to me frrom their explanation why those statements should work.

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last modified January 16, 2010