Question

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

Liliane has $20\%$ more soda than Alice.

Liliane has $25\%$ more soda than Alice.

Liliane has $45\%$ more soda than Alice.

Liliane has $75\%$ more soda than Alice.

Liliane has $100\%$ more soda than Alice.

Solution:

Let $x$ be the number of gallons of soda that Jacqueline has. Then Alice has $1.25x$ gallons, and Liliane has $1.5x$ gallons.

Therefore, the relationship can be found by dividing the amount of soda that each has to yield $\dfrac{1.5x}{1.25x} = 1.2,$ which mean Liliane has $20\%$ more soda.

Thus, A is the correct answer.

2018 AMC 10A Problem 2

Solution:

Problem 2 in Other Years