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 "2014 AMC 8 Problems/Problem 7"

(→‎Solution 2)
(→‎Solution 2)
Line 8: Line 8:
 
==Solution 2==
 
==Solution 2==
  
−
To make the amount of boys and girls equal, 28-4 = 24.  24/2 = 12.  The girls would need to be 12 + the 4 that we subtracted = 16. The boys would be 12.  The ratio of girls to boys would be 16:12, but simplified would be 4:3.
+
To make the amount of boys and girls equal, 28 - 4 = 24.  24/2 = 12.  The girls would need to be 12 + the 4 that we subtracted = 16. The boys would be 12.  The ratio of girls to boys would be 16 : 12, but simplified would be 4 : 3.  Thus, the answer is <math>16:12=\boxed{\textbf{(B)}~4:3}</math>.
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2014|num-b=6|num-a=8}}
 
{{AMC8 box|year=2014|num-b=6|num-a=8}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 20:20, 20 December 2021

Problem

There are four more girls than boys in Ms. Raub's class of $28$ students. What is the ratio of number of girls to the number of boys in her class?

$\textbf{(A) }3 : 4\qquad\textbf{(B) }4 : 3\qquad\textbf{(C) }3 : 2\qquad\textbf{(D) }7 : 4\qquad \textbf{(E) }2 : 1$

Solution 1

We can set up an equation with $x$ being the number of girls in the class. The number of boys in the class is equal to $x-4$. Since the total number of students is equal to $28$, we get $x+x-4=28$. Solving this equation, we get $x=16$. There are $16-4=12$ boys in our class, and our answer is $16:12=\boxed{\textbf{(B)}~4:3}$.

Solution 2

To make the amount of boys and girls equal, 28 - 4 = 24. 24/2 = 12. The girls would need to be 12 + the 4 that we subtracted = 16. The boys would be 12. The ratio of girls to boys would be 16 : 12, but simplified would be 4 : 3. Thus, the answer is $16:12=\boxed{\textbf{(B)}~4:3}$.

See Also

2014 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 6 		Followed by
Problem 8
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2014_AMC_8_Problems/Problem_7&oldid=168169"