Try this beautiful problem from Algebra based on Quadratic equation.

## Algebra based on Quadratic equation – AMC-8, 2009 – Problem 23

On the last day of school, Mrs. Awesome gave jelly beans to her class. She gave each boy as many jelly beans as there were boys in the class. She gave each girl as many jelly beans as there were girls in the class. She brought 400 jelly beans, and when she finished, she had six jelly beans left. There were two more boys than girls in her class. How many students were in her class?

- $34$
- $28$
- $25$

**Key Concepts**

Algebra

quadratic equation

Factorization

## Check the Answer

But try the problem first…

Answer:$28$

AMC-8 (2009) Problem 23

Pre College Mathematics

## Try with Hints

First hint

Let the number of girls be x

so the number of boys be x+2

Can you now finish the problem ……….

Second Hint

She gave away 400-6=394 jelly beans

\(x^2 + (x+2)^2=394\)

can you finish the problem……..

Final Step

Let the number of girls be x

so the number of boys be x+2

she gave each girl x jellybeans and each boy x+2 jellybeans,

Therefore she gave total number of jelly beans to girls be \(x^2\)

Therefore she gave total number of jelly beans to boys be \((x+2)^2\)

She gave away 400-6=394 jelly beans

\(x^2 + (x+2)^2=394\)

\(\Rightarrow x^2 + x^2 +4x+4=394\)

\(\Rightarrow 2x^2 +4x-390=0\)

\(\Rightarrow x^2 +2x -195=0\)

\((x+15)(x-13)=0\)

i.e x=-15 , 13 (we neglect negetive as number of students can not be negetive )

Therefore x=13 i.e number os girls be 13 and number of boys be 13+2=15

total number of students ne 13+15=28

## Other useful links

- https://www.youtube.com/watch?v=w0Y2oXoyEEQ
- https://www.cheenta.com/area-of-square-and-circle-amc-8-2011-problem-25/