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 "1987 AJHSME Problems/Problem 16"

m
m (→‎Problem)
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
 
==Problem==
 
==Problem==
  
−
Joyce made <math>12</math> of her first <math>30</math> shots in the first three games of this basketball game, so her seasonal shooting [[average]] was <math>40\% </math>.  In her next game, she took <math>10</math> shots and raised her seasonal shooting average to <math>50\% </math>.  How many of these <math>10</math> shots did she make?
+
Joyce made <math>12</math> of her first <math>30</math> shots in the first three games of this basketball season, so her seasonal shooting [[average]] was <math>40\% </math>.  In her next game, she took <math>10</math> shots and raised her seasonal shooting average to <math>50\% </math>.  How many of these <math>10</math> shots did she make?
  
 
<math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8</math>
 
<math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8</math>
Line 15: Line 15:
 
{{AJHSME box|year=1987|num-b=15|num-a=17}}
 
{{AJHSME box|year=1987|num-b=15|num-a=17}}
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]
 +
{{MAA Notice}}

Latest revision as of 22:04, 9 June 2024

Problem

Joyce made $12$ of her first $30$ shots in the first three games of this basketball season, so her seasonal shooting average was $40\%$. In her next game, she took $10$ shots and raised her seasonal shooting average to $50\%$. How many of these $10$ shots did she make?

$\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8$

Solution

After the fourth game, she took $40$ shots, $50\%$ of which she made, so she made $40\times .5=20$ shots. Twelve of them were made in the first three games, so in the last game she made $20-12=8$ shots.

$\boxed{\text{E}}$

See Also

1987 AJHSME (Problems • Answer Key • Resources)
Preceded by
Problem 15 		Followed by
Problem 17
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. AMC Logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1987_AJHSME_Problems/Problem_16&oldid=220270"