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2022 AMC 8 Problems/Problem 5

Revision as of 00:24, 9 January 2023 by Sohumuttamchandani (talk | contribs) (→‎Solution (Written))

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

We have the following perimeter that the cat is now $5$ years old (born $5$ years ago) and the younger sister Bella was born $6+5 = 11$ years ago. Since we know the sum of the three children, we can calculate the age of Anna as $30 - 11 - 5 = 14$. The question asks for difference in age between the sisters which is $14 - 11 = \boxed{(C) 3}$

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

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