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 amout 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 the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per glass on the second day?
a. .15
b. .2
c. .3
d. .4
e. .45

On the 1st day, 1 unit of orange juice was mixed with 1 unit of water.
So, total amount of orangeade = (1 + 1) = 2 units
If each glass contained n units of orangeade, total number of glasses sold = 2/n
As price per glass was $0.60, total revenue on the 1st day = (0.60)*(2/n)

On the 2nd day, 1 unit of orange juice was mixed with 2 units of water.
So, total amount of orangeade = (1 + 2) = 3 units
If each glass contained n units of orangeade, total number of glasses sold = 3/n
Total revenue on the 2nd day = Total revenue on the 1st day = (0.60)*(2/n)

Hence, price per glass on the 2nd day = (Total revenue)/(number of glasses sold) = (0.60)*(2/n)/(3/n) = (0.60)*(2/n)*(n/3) = (0.20)*2 = 0.40

The correct answer is D.

faraz_jeddah wrote:Can you give a deeper explanation on how you get 2/n?

Let us assume on the 1st day, x liters of orange juice was mixed with x liters of water.
So, total amount of orangeade = (x + x) = 2x liters
If each glass contained n liters of orangeade, total number of glasses sold = 2x/n

For simplicity, I've assumed x = 1 as it doesn't matter how much juice was mixed with how much water as long as they are same. But if you are not convinced, we can proceed using with x in the same way.

As price per glass was $0.60, total revenue on the 1st day = $(0.60)*(2x/n)

On the 2nd day, x liters of orange juice was mixed with 2x liters of water.
So, total amount of orangeade = (x + 2x) = 3x liters
If each glass contained n liters of orangeade, total number of glasses sold = 3x/n
Total revenue on the 2nd day = Total revenue on the 1st day = (0.60)*(2x/n)

Hence, price per glass on the 2nd day = (Total revenue)/(number of glasses sold) = (0.60)*(2x/n)/(3x/n) = (0.60)*(2x/n)*(n/3x) = (0.20)*2 = 0.40

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In fact, if you understand the underlined part, then you'll see that we can assume n = 1 too. That means, on the first day 1 glass of juice was mixed with 1 glass of water to get 2 glasses of orangeade. So, total revenue on 1st day = $(0.60)*2 = $1.20

Now, on the second day 1 glass of juice was mixed with 2 glasses of water to get 3 glasses of orangeade. As the revenue on the 2nd day is also $1.20, the price per glass must be $1.20/3 = $0.40

Hope that helps.