Difference between revisions of "2014 AMC 8 Problems/Problem 7"

Revision as of 01:57, 24 December 2022

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

Let $g$ being the number of girls in the class. The number of boys in the class is equal to $g-4$ . Since the total number of students is equal to $28$ , we get $g+g-4=28$ . Solving this equation, we get $g=16$ . 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 4 : 3.

~MiracleMaths

Video Solution

https://youtu.be/fjbcgj5W30E ~savannahsolver

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.

@@ Line 4: / Line 4: @@
 <math>\textbf{(A) }3 : 4\qquad\textbf{(B) }4 : 3\qquad\textbf{(C) }3 : 2\qquad\textbf{(D) }7 : 4\qquad \textbf{(E) }2 : 1</math>
 ==Solution 1==
-We can set up an equation with <math>x</math> being the number of girls in the class. The number of boys in the class is equal to <math>x-4</math>. Since the total number of students is equal to <math>28</math>, we get <math>x+x-4=28</math>. Solving this equation, we get <math>x=16</math>. There are <math>16-4=12</math> boys in our class, and our answer is <math>16:12=\boxed{\textbf{(B)}~4:3}</math>.
+Let <math>g</math> being the number of girls in the class. The number of boys in the class is equal to <math>g-4</math>. Since the total number of students is equal to <math>28</math>, we get <math>g+g-4=28</math>. Solving this equation, we get <math>g=16</math>. There are <math>16-4=12</math> boys in our class, and our answer is <math>16:12=\boxed{\textbf{(B)}~4:3}</math>.
 ==Solution 2==

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