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

Latest revision as of 09:21, 18 August 2024

Problem

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?

$\textbf{(A) }$ 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 1

Let's assume that Jacqueline has $1$ gallon(s) 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 $\boxed{\textbf{(A)}}$ .

Solution 2

WLOG, lets use $4$ gallons instead of $1$ . When you work it out, you get $6$ gallons and $5$ gallons. We have $6 - 5 = 1$ is $20\%$ of $5$ . Thus, we reach $\boxed{\textbf{(A)}}$ .

~Ezraft

Solution 3

If Jacqueline has $x$ gallons of soda, Alice has $1.25x$ gallons, and Liliane has $1.5x$ gallons. Thus, the answer is $\frac{1.5}{1.25}=1.2$ $=>$ Liliane has $20\%$ more soda. Our answer is $\boxed{\textbf{(A)}}$ .

~lakecomo224 (minor edits made by <B+)

Video Solution (HOW TO THINK CREATIVELY!)

https://youtu.be/zMeYuDelX8E

Education, the Study of Everything

Video Solutions

https://youtu.be/vO-ELYmgRI8

https://youtu.be/jx9RnjX9g-Q

~savannahsolver

2018 AMC 10A (Problems • Answer Key • Resources)
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All AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

@@ Line 22: / Line 22: @@
 == Solution 3 ==
-If Jacqueline has <math>x</math> gallons of soda, Alice has <math>1.25x</math> gallons, and Liliane has <math>1.5x</math> gallons. Thus, the answer is <math>\frac{1.5}{1.25}=1.2</math> -> Liliane has <math>20\%</math> more soda. Our answer is <math>\boxed{\textbf{(A)}}</math>.
+If Jacqueline has <math>x</math> gallons of soda, Alice has <math>1.25x</math> gallons, and Liliane has <math>1.5x</math> gallons. Thus, the answer is <math>\frac{1.5}{1.25}=1.2</math> <math>=></math> Liliane has <math>20\%</math> more soda. Our answer is <math>\boxed{\textbf{(A)}}</math>.
-~lakecomo224
+~lakecomo224 (minor edits made by <B+)
 ==Video Solution (HOW TO THINK CREATIVELY!)==

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