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Brand X soda advertises, ``We will give you 20% more soda than Brand Y for a total price that is 10% less than Brand Y's price!'' What is the ratio of the unit price of Brand X soda to the unit price of Brand Y soda? Express your answer as a common fraction.

 Apr 26, 2023
 #1
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Let the price of one unit of Brand Y soda be $y$, so the price of one unit of Brand X soda is $0.9y$.

According to the advertisement, the quantity of soda in one unit of Brand X soda is 20% more than the quantity of soda in one unit of Brand Y soda. Therefore, the ratio of the quantities of soda in one unit of Brand X and Brand Y soda is:

(1 + 0.2)/1 = 1.

So, one unit of Brand X soda has 1.2 times as much soda as one unit of Brand Y soda.

Therefore, the ratio of the unit price of Brand X soda to the unit price of Brand Y soda is:

0.9y/(y/1.2) = 0.9*y*1.2/y = 

$\frac{0.9y}{y/1.2} = \frac{0.9y \cdot 1.2}{y} = 27/25

 Apr 26, 2023
 #2
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Let the amount of soda of Brand Y ==y
Let the total price of Brand Y soda ==p
Unit price of Brand Y soda ==p / y

 

The amount of soda of Brand X ==1.20y
The total price of Brand X ==0.90p
Unit price of Brand X ==0.90p / 1.20y

 

The ratio of the unit price of Brand X to Brand Y is:
[0.90p / 1.20y] / [p / y] ==3 / 4

 Apr 26, 2023
 #3
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Let p be the price of a unit of Brand Y soda and q be the amount of Brand Y soda in a can.

Let r be the price of a unit of Brand X soda and s be the amount of Brand X soda in a can.

We are given that s=1.2q and r=0.9p.

Therefore, the ratio of the unit price of Brand X soda to the unit price of Brand Y soda is:

r/p = 0.9p/p = 0.9 = 9/10.

 Apr 26, 2023

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