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

Difference between revisions of "1959 AHSME Problems/Problem 29"

(Created page with "== Problem 29== On a examination of <math>n</math> questions a student answers correctly <math>15</math> of the first <math>20</math>. Of the remaining questions he answers on...")
 
(→‎Solution)
Line 7: Line 7:
  
 
==Solution==
 
==Solution==
−
To calculate the student's score in terms of <math>x</math>, you can write the following equation:
+
To calculate the student's score in terms of <math>n</math>, you can write the following equation:
−
<math>(n-20)/3 + 45 = 3n/2</math>. Simplify to get <math>n=55</math>, so there is one solution.
+
 
 +
<math>\frac{n-20}{3} + 45 = 3n/2</math>. Simplify to get <math>n=55</math>, so there is one solution.

Revision as of 14:13, 16 July 2024

Problem 29

On a examination of $n$ questions a student answers correctly $15$ of the first $20$. Of the remaining questions he answers one third correctly. All the questions have the same credit. If the student's mark is 50%, how many different values of $n$ can there be? $\textbf{(A)}\ 4 \qquad\textbf{(B)}\ 3\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}\ 1\qquad\textbf{(E)}\ \text{the problem cannot be solved}$

Solution

Solution

To calculate the student's score in terms of $n$, you can write the following equation:

$\frac{n-20}{3} + 45 = 3n/2$. Simplify to get $n=55$, so there is one solution.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1959_AHSME_Problems/Problem_29&oldid=222842"