2020 AMC 8 Problems/Problem 15

1 Problem
2 Solution 1
3 Solution 2
4 Solution 3
5 Solution 4
6 Solution 5
7 Solution 6
8 Video Solution by NiuniuMaths (Easy to understand!)
9 Video Solution by Math-X (First understand the problem!!!)
10 Video Solution (🚀Very Fast🚀)
11 Video Solution
12 Video Solution
13 Video Solution by Interstigation
14 See also

Problem

Suppose $15\%$ of $x$ equals $20\%$ of $y.$ What percentage of $x$ is $y?$

$\textbf{(A) }5 \qquad \textbf{(B) }35 \qquad \textbf{(C) }75 \qquad \textbf{(D) }133 \frac13 \qquad \textbf{(E) }300$

Solution 1

Since $20\% = \frac{1}{5}$ , multiplying the given condition by $5$ shows that $y$ is $15 \cdot 5 = \boxed{\textbf{(C) }75}$ percent of $x$ .

Solution 2

Letting $x=100$ (without loss of generality), the condition becomes $0.15\cdot 100 = 0.2\cdot y \Rightarrow 15 = \frac{y}{5} \Rightarrow y=75$ . Clearly, it follows that $y$ is $75\%$ of $x$ , so the answer is $\boxed{\textbf{(C) }75}$ .

Solution 3

We have $15\%=\frac{3}{20}$ and $20\%=\frac{1}{5}$ , so $\frac{3}{20}x=\frac{1}{5}y$ . Solving for $y$ , we multiply by $5$ to give $y = \frac{15}{20}x = \frac{3}{4}x$ , so the answer is $\boxed{\textbf{(C) }75}$ .

Solution 4

We are given $0.15x = 0.20y$ , so we may assume without loss of generality that $x=20$ and $y=15$ . This means $\frac{y}{x}=\frac{15}{20}=\frac{75}{100}$ , and thus the answer is $\boxed{\textbf{(C) }75}$ .

Solution 5

$15\%$ of $x$ is $0.15x$ , and $20\%$ of $y$ is $0.20y$ . We put $0.15x$ and $0.20y$ into an equation, creating $0.15x = 0.20y$ because $0.15x$ equals $0.20y$ . Solving for $y$ , dividing $0.2$ to both sides, we get $y = \frac{15}{20}x = \frac{3}{4}x$ , so the answer is $\boxed{\textbf{(C) }75}$ .

Solution 6

$15\%$ of $x$ can be written as $\frac{15}{100}x$ , or $\frac{15x}{100}$ . $20\%$ of $y$ can similarly be written as $\frac{20}{100}y$ , or $\frac{20y}{100}$ . So now, $\frac{15x}{100} = \frac{20y}{100}$ . Using cross-multiplication, we can simplify the equation as: $1500x = 2000y$ . Dividing both sides by $500$ , we get: $3x = 4y$ . $\frac{3}{4}$ is the same thing as $75\%$ , so the answer is $\boxed{\textbf{(C) }75}$ .

Video Solution by NiuniuMaths (Easy to understand!)

https://www.youtube.com/watch?v=bHNrBwwUCMI

~NiuniuMaths

Video Solution by Math-X (First understand the problem!!!)

https://youtu.be/UnVo6jZ3Wnk?si=fRl03D9Q1KAdDtXz&t=2346

~Math-X

Video Solution (🚀Very Fast🚀)

https://youtu.be/8LyGag4DOzo

~Education, the Study of Everything

Video Solution

https://youtu.be/mjS-PHTw-GE

~savannahsolver

Video Solution

https://youtu.be/xjwDsaRE_Wo

Video Solution by Interstigation

https://youtu.be/YnwkBZTv5Fw?t=665

~Interstigation

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2020 AMC 8 Problems/Problem 15

Contents

Problem

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Video Solution by NiuniuMaths (Easy to understand!)

Video Solution by Math-X (First understand the problem!!!)

Video Solution (🚀Very Fast🚀)

Video Solution

Video Solution

Video Solution by Interstigation

See also