On a certain day, orangeade was made

On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days all the orangeade that was made was sold. If the revenue from selling the orangeade was sold at $0.60 per glass on the first day. what was the price per glass on the second day?

2 Explanations

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Let´s express it as a ratio:

O:W
1:1 -> # of "volume units" = 2 (day1)
1:2 -> # of "volume units" = 3 (day2)

Notice also the revenue formula:

revenue = #units * price per unit

So, being the revenue equal at both days:

revenue day 1 = revenue day 2

#"vol. units" d1 * price per unit d1 = #"vol. units" d2 * price per unit d2

2 * 0,60 = 3 * Pd2
(0,60 * 2) / 3 = 0,20 * 2 = 0,40

Jan 25, 2015 • Comment

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Mike McGarry, Magoosh Tutor

Dec 27, 2013 • Comment

Mr Tim

I understand this approach, but everytime I try to set it up, my mind thinks of doing a proportion--which always goes to the wrong answer (i.e.: 2/0.60 = 3/x). Any tips?

Dec 4, 2014 • Reply

That's an easy mistake to make! If you are setting up a proportion, make sure you think about whether your result makes sense. The orangeade with the higher concentration of OJ should be more expensive.

The proportion 2/0.60 = 3/x doesn't work because what do 2 and 3 represent? They are the amounts of orangeade. And we know the revenue both days is the same.

We COULD set up a proportion, but it would be:

(1/2) / .60 = (1/3) / x

The first day, the orangeade is 1/2 OJ, and the 2nd day, it's 1/3 OJ.

This makes sense, because the ratios of the concentration of OJ to the cost should be the same.

So when you have a proportion, take a moment to think about whether your answer makes sense. If it doesn't, then it's likely you should have used multiplication (as in the video) instead of division, or you should have flipped some of the values (as I took 1/2 and 1/3 instead of 2 and 3).

I hope that helps! :)

Feb 6, 2015 • Reply