# Birthdays

In the classroom, students always give candy to their classmates on their birthdays. The birthday person always gives each one candy, and he does not give himself. A total of 650 candies were distributed in the class per year. How many students are in the class? (Note: All students in the class had a birthday on the day of the class. )

Result

n =  26

#### Solution:

$n*(n-1)=650 \ \\ \ \\ n \cdot \ (n-1)=650 \ \\ n^2 -n -650=0 \ \\ \ \\ a=1; b=-1; c=-650 \ \\ D=b^2 - 4ac=1^2 - 4\cdot 1 \cdot (-650)=2601 \ \\ D>0 \ \\ \ \\ n_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 1 \pm \sqrt{ 2601 } }{ 2 } \ \\ n_{1,2}=\dfrac{ 1 \pm 51 }{ 2 } \ \\ n_{1,2}=0.5 \pm 25.5 \ \\ n_{1}=26 \ \\ n_{2}=-25 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (n -26) (n +25)=0 \ \\ \ \\ n=n_{1}=26$

Checkout calculation with our calculator of quadratic equations.

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

## Next similar math problems:

1. Solve 3
Solve quadratic equation: (6n+1) (4n-1) = 3n2
2. The product
The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number
3. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
4. Roots
Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
5. Product
The product of two consecutive odd numbers is 8463. What are this numbers?
Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
7. Calculation
How much is sum of square root of six and the square root of 225?
8. Discriminant
Determine the discriminant of the equation: ?
9. Equation
Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
Solve quadratic equation: 2x2-58x+396=0
11. Apples
A 2 kg of apples cost a certain sum of money. This sum is equal to the amount of kilograms for which we pay 72 CZK. How much is 1 kg of apples?
12. Solve equation
solve equation: ?
13. Fraction
For what x expression ? equals zero?
14. Water reservoir
The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one.
15. Expression with powers
If x-1/x=5, find the value of x4+1/x4
16. Children
The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group?
17. Equation 23
Find value of unknown x in equation: x+3/x+1=5 (problem finding x)