Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

1954 AHSME Problems/Problem 3

Revision as of 12:35, 6 June 2016 by Katzrockso (talk | contribs) (Created page with "== Problem 3== If <math>x</math> varies as the cube of <math>y</math>, and <math>y</math> varies as the fifth root of <math>z</math>, then <math>x</math> varies as the nth po...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem 3

If $x$ varies as the cube of $y$, and $y$ varies as the fifth root of $z$, then $x$ varies as the nth power of $z$, where n is:

$\textbf{(A)}\ \frac{1}{15} \qquad\textbf{(B)}\ \frac{5}{3} \qquad\textbf{(C)}\ \frac{3}{5} \qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 8$

Solution

$x=k\cdot y^3$, $y=j\cdot z^{\frac{1}{5}}\implies y^3=j^3\cdot z^{\frac{3}{5}}$, so $x=k\cdot j^3\cdot z^{\frac{3}{5}}$, $\fbox{C}$

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1954_AHSME_Problems/Problem_3&oldid=78808"