Difference between revisions of "2024 AMC 8 Problems/Problem 19"

Revision as of 17:46, 25 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?

(A) $0$ (B) $\frac{1}{5}$ (C) $\frac{4}{15}$ (D) $\frac{1}{3}$ (E) $\frac{2}{5}$

Solution

Jordan has $10$ high top sneakers, and $6$ white sneakers. We would want as many white high-top sneakers as possible, so we set $6$ high-top sneakers to be white. Then, we have $10-6=4$ red high-top sneakers, so the answer is $\boxed{\dfrac{4}{15}}.$

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.

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

https://www.youtube.com/watch?v=eYnLh_SGy7c

~Math-X

@@ Line 10: / Line 10: @@
 ==Solution 1==
-We first start by finding the amount of red and white sneakers. 3/5 times 15=9 red sneakers, so 6 are white sneakers. Then 2/3 times 15=10 are high top sneakers, so 5 are low top sneakers.
+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.
 ==Video Solution by Math-X (First fully understand the problem!!!)==

Page

Toolbox

Search