How Cheenta works to ensure student success?
Explore the Back-Story
Problems and Solutions from CMI Entrance 2022.  Learn More 

Math Kangaroo (Benjamin) 2014 Problem No 24

Try this beautiful Problem based on simple Algebra appeared in Math Kangaroo (Benjamin) 2014 Problem 24.

Math Kangaroo (Benjamin) 2014 | Problem No 24


Grandma gives 180 marbles to her ten grandchildren. No two children get the same amount of marbles. Anna gets the most. What is the minimum number of marbles that Anna could get?

  • 19
  • 20
  • 21
  • 22
  • 23

Key Concepts


Arithmetic

Equation solving

Algebra

Suggested Book | Source | Answer


Algebra by Gelfand

Math Kangaroo (Benjamin), 2014

$23$

Try with Hints


Hint 1

Here

Number of children is $10$.
Number of marbles is $180$.
And Anna gets the most and no 2 children gets the same number of marbles.

Hint 2

Let us assume that Anna could get $x$ marbles and also the other 9 children receiving 1 less each step. Apply the condition to construct the equation

Hint 3

The equation will be-

$x$+$x$-$1$+$x$-$2$+$x$-$3$+$x$-$4$+$x$-$5$+$x$-$6$+$x$-$7$+$x$-$8$+$x$-$9$=$180$

Now solve for $x$.

Hint 4


So, Anna can have $23$ marbles.

Subscribe to Cheenta at Youtube


Try this beautiful Problem based on simple Algebra appeared in Math Kangaroo (Benjamin) 2014 Problem 24.

Math Kangaroo (Benjamin) 2014 | Problem No 24


Grandma gives 180 marbles to her ten grandchildren. No two children get the same amount of marbles. Anna gets the most. What is the minimum number of marbles that Anna could get?

  • 19
  • 20
  • 21
  • 22
  • 23

Key Concepts


Arithmetic

Equation solving

Algebra

Suggested Book | Source | Answer


Algebra by Gelfand

Math Kangaroo (Benjamin), 2014

$23$

Try with Hints


Hint 1

Here

Number of children is $10$.
Number of marbles is $180$.
And Anna gets the most and no 2 children gets the same number of marbles.

Hint 2

Let us assume that Anna could get $x$ marbles and also the other 9 children receiving 1 less each step. Apply the condition to construct the equation

Hint 3

The equation will be-

$x$+$x$-$1$+$x$-$2$+$x$-$3$+$x$-$4$+$x$-$5$+$x$-$6$+$x$-$7$+$x$-$8$+$x$-$9$=$180$

Now solve for $x$.

Hint 4


So, Anna can have $23$ marbles.

Subscribe to Cheenta at Youtube


Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy
Cheenta

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com
magic-wand