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 "2022 AMC 8 Problems/Problem 5"

(→‎Solution (Written))
(→‎Solution)
Line 6: Line 6:
  
 
==Solution==
 
==Solution==
−
We have the following perimeter that the cat is now <math>5</math> years old (born <math>5</math> years ago) and the younger sister Bella was born <math>6+5 = 11</math> years ago. Since we know the sum of the three children, we can calculate the age of Anna as <math>30 - 11 - 5 = 14</math>. The question asks for difference in age between the sisters which is <math>14 - 11 = \boxed{(C) 3}</math>
+
 
  
 
Five years ago, Bella was <math>6</math> years old, and the kitten was <math>0</math> years old.
 
Five years ago, Bella was <math>6</math> years old, and the kitten was <math>0</math> years old.
Line 15: Line 15:
  
 
~MRENTHUSIASM
 
~MRENTHUSIASM
 +
 
==Video Solution==
 
==Video Solution==
 
https://www.youtube.com/watch?v=Ij9pAy6tQSg&t=323
 
https://www.youtube.com/watch?v=Ij9pAy6tQSg&t=323

Revision as of 00:24, 9 January 2023

Problem

Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned $6$ years old, she received a newborn kitten as a birthday present. Today the sum of the ages of the two children and the kitten is $30$ years. How many years older than Bella is Anna?

$\textbf{(A) } 1 \qquad \textbf{(B) } 2 \qquad \textbf{(C) } 3 \qquad \textbf{(D) } 4 \qquad \textbf{(E) } ~5$

Solution

Five years ago, Bella was $6$ years old, and the kitten was $0$ years old.

Today, Bella is $11$ years old, and the kitten is $5$ years old. It follows that Anna is $30-11-5=14$ years old.

Therefore, Anna is $14-11=\boxed{\textbf{(C) } 3}$ years older than Bella.

~MRENTHUSIASM

Video Solution

https://www.youtube.com/watch?v=Ij9pAy6tQSg&t=323

~Interstigation

Video Solution

https://youtu.be/WY0m0jAj__Y

~savannahsolver

Video Solution

https://youtu.be/Q0R6dnIO95Y?t=212

~STEMbreezy

See Also

2022 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 4 		Followed by
Problem 6
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=2022_AMC_8_Problems/Problem_5&oldid=186121"