Try this beautiful Problem based on simple Algebra appeared in Math Kangaroo (Benjamin) 2014 Problem 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?
Arithmetic
Equation solving
Algebra
Algebra by Gelfand
Math Kangaroo (Benjamin), 2014
$23$
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.
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
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 $x$.
So, Anna can have $23$ marbles.
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