Difference between revisions of "2018 AMC 10A Problems/Problem 2"

Revision as of 14:02, 8 February 2018

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 Alica have?

$\textbf{(A) }$ Liliane has $20\%$ more soda than Alice. $\textbf{(B) }$ Liliane has $25\%$ more soda than Alice. $\textbf{(C) }$ Liliane has $45\%$ more soda than Alice. $\textbf{(D) }$ Liliane has $75\%$ more soda than Alice. $\textbf{(E) }$ Liliane has $100\%$ more soda than Alice.

Solution

Let's assume that Jacqueline has $1$ gallon of soda. Then Alice has $1.25$ gallons and Liliane has $1.5$ gallons. Doing division, we find out that $\frac{1.5}{1.25}=1.2$ , which means that Liliane has 20% more soda. Therefore, the answer is $\boxed{\textbf{(A)}}$

@@ Line 7: / Line 7: @@
 <math>\textbf{(D) }</math>Liliane has <math>75\%</math> more soda than Alice.
 <math>\textbf{(E) }</math>Liliane has <math>100\%</math> more soda than Alice.
+===Solution===
+Let's assume that Jacqueline has <math>1</math> gallon of soda. Then Alice has <math>1.25</math> gallons and Liliane has <math>1.5</math> gallons. Doing division, we find out that <math>\frac{1.5}{1.25}=1.2</math>, which means that Liliane has 20% more soda. Therefore, the answer is <math>\boxed{\textbf{(A)}}</math>

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Difference between revisions of "2018 AMC 10A Problems/Problem 2"

Revision as of 14:02, 8 February 2018

Solution