Difference between revisions of "2014 AMC 8 Problems/Problem 7"
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| − | 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? | + | ==Problem== |
| + | There are four more girls than boys in Ms. Raub's class of <math>28</math> students. What is the ratio of number of girls to the number of boys in her class? | ||
<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> | <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== | ||
| + | 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== | ||
| + | |||
| + | 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 (CREATIVE THINKING)== | ||
| + | https://youtu.be/lKIgQdAOmyU | ||
| + | |||
| + | ~Education, the Study of Everything | ||
| + | |||
| + | |||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/fjbcgj5W30E ~savannahsolver | ||
==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}} | ||
Latest revision as of 14:14, 18 June 2024
Contents
Problem
There are four more girls than boys in Ms. Raub's class of 
students. What is the ratio of number of girls to the number of boys in her class?
Solution 1
Let 
being the number of girls in the class. The number of boys in the class is equal to 
. Since the total number of students is equal to , we get 
. Solving this equation, we get 
. There are 
boys in our class, and our answer is 
.
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 (CREATIVE THINKING)
~Education, the Study of Everything
Video Solution
https://youtu.be/fjbcgj5W30E ~savannahsolver
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. 
