2024 AMC 8 Problems/Problem 19: Difference between revisions
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==Problem== | ==Problem== | ||
Jordan owns | Jordan owns 15 pairs of sneakers. Three fifths of the pairs are red and the rest are white. Two thirds of the pairs are high-top and the rest are low-top. The red high-top sneakers make up a fraction of the collection. What is the least possible value of this fraction? | ||
(A) | <math>\textbf{(A) } 0\qquad\textbf{(B) } \dfrac{1}{5} \qquad\textbf{(C) } \dfrac{4}{15} \qquad\textbf{(D) } \dfrac{1}{3} \qquad\textbf{(E) } \dfrac{2}{5}</math> | ||
==Solution== | ==Solution== | ||
Revision as of 12:27, 26 January 2024
Problem
Jordan owns 15 pairs of sneakers. Three fifths of the pairs are red and the rest are white. Two thirds of the pairs are high-top and the rest are low-top. The red high-top sneakers make up a fraction of the collection. What is the least possible value of this fraction?
Solution
Jordan has 
high top sneakers, and 
white sneakers. We would want as many white high-top sneakers as possible, so we set high-top sneakers to be white. Then, we have 
red high-top sneakers, so the answer is 
Solution 1
We first start by finding the amount of red and white sneakers. 3/5 * 15=9 red sneakers, so 6 are white sneakers. Then 2/3 * 15=10 are high top sneakers, so 5 are low top sneakers. Now think about 15 slots and the first 10 are labeled high top sneakers. if we insert the last 5 sneakers as red sneakers there are 4 leftover over red sneakers. Putting those four sneakers as high top sneakers we have are answer as C or
-Multpi12
Video Solution 1 by Math-X (First fully understand the problem!!!)
https://www.youtube.com/watch?v=eYnLh_SGy7c
~Math-X
