2022 AMC 8 Problems/Problem 5: Difference between revisions
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Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned <math>6</math> 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 <math>30</math> years. How many years older than Bella is Anna? | Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned <math>6</math> 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 <math>30</math> years. How many years older than Bella is Anna? | ||
<math>\textbf{(A)} | <math>\textbf{(A) } 1 \qquad \textbf{(B) } 2 \qquad \textbf{(C) } 3 \qquad \textbf{(D) } 4 \qquad \textbf{(E) } ~5</math> | ||
==Solution== | ==Solution== | ||
Five years ago, Bella was <math>6</math> years old, and the kitten was <math>0</math> years old. | |||
Today, Bella is <math>11</math> years old, and the kitten is <math>5</math> years old. It follows that Anna is <math>30-11-5=14</math> years old. | |||
Therefore, Anna is <math>14-11=\boxed{\textbf{(C) } 3}</math> years older than Bella. | |||
~MRENTHUSIASM | ~MRENTHUSIASM | ||
==Video Solution (A Clever Explanation You’ll Get Instantly)== | |||
https://youtu.be/tYWp6fcUAik?si=V8hv_zOn_zYOi9E5&t=505 | |||
~hsnacademy | |||
==Video Solution by Math-X (First understand the problem!!!)== | |||
https://youtu.be/oUEa7AjMF2A?si=AeqPj9sQgiBU3_lL&t=585 | |||
~Math-X | |||
==Video Solution (CREATIVE THINKING!!!)== | |||
https://youtu.be/NuRFgRUpV7o | |||
~Education, the Study of Everything | |||
==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 | |||
==Video Solution== | |||
https://youtu.be/Cb5as-fLejk | |||
~harungurcan | |||
==Video Solution by Dr. David== | |||
https://youtu.be/Sc5F9WeEhE8 | |||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2022|num-b=4|num-a=6}} | {{AMC8 box|year=2022|num-b=4|num-a=6}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
[[Category:Introductory Algebra Problems]] | |||
Latest revision as of 16:47, 4 June 2025
Problem
Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned 
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 
years. How many years older than Bella is Anna?
Solution
Five years ago, Bella was years old, and the kitten was 
years old.
Today, Bella is 
years old, and the kitten is 
years old. It follows that Anna is 
years old.
Therefore, Anna is 
years older than Bella.
~MRENTHUSIASM
Video Solution (A Clever Explanation You’ll Get Instantly)
https://youtu.be/tYWp6fcUAik?si=V8hv_zOn_zYOi9E5&t=505 ~hsnacademy
Video Solution by Math-X (First understand the problem!!!)
https://youtu.be/oUEa7AjMF2A?si=AeqPj9sQgiBU3_lL&t=585
~Math-X
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Video Solution
https://www.youtube.com/watch?v=Ij9pAy6tQSg&t=323
~Interstigation
Video Solution
~savannahsolver
Video Solution
https://youtu.be/Q0R6dnIO95Y?t=212
~STEMbreezy
Video Solution
~harungurcan
Video Solution by Dr. David
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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: Unable to save thumbnail to destination
