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2018 AMC 10A Problem 2

Problem 2 of 25EasierAlgebra

Liliane has 50%50\% more soda than Jacqueline, and Alice has 25%25\% more soda than Jacqueline. What is the relationship between the amounts of soda that Liliane and Alice have?

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Solution

Let xx be the number of gallons of soda that Jacqueline has. Then Alice has 1.25x1.25x gallons, and Liliane has 1.5x1.5x gallons. Therefore, the relationship can be found by dividing the amount of soda that each has to yield 1.5x1.25x=1.2,\dfrac{1.5x}{1.25x}=1.2, which means Liliane has 20%20\% more soda than Alice. Thus, A is the correct answer.

More practice

Concepts: percentage · ratio and proportion

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.