every student in a second grade class sends a valentine to each of the other students in the class, for a total of 306 valentines.How many students are in the class.

The square root of 306 is about 17.5.

So I multiplied 17 * 17 and got 289 Valentines.

There must be 18 students in the class -- and the each sent 17 cards.

i need help on extended response

18 Students is the answer you exclude the student passing out the Valentines. So 18 students received 17 valentines...

To find the number of students in the second-grade class, we can use the formula for the sum of the first n natural numbers:

Sum = (n * (n + 1)) / 2

In this case, the sum is 306 valentines, which represents the total number of valentines exchanged between the students.

Let's solve the equation:

(n * (n + 1)) / 2 = 306

Multiply both sides of the equation by 2 to eliminate the fraction:

n * (n + 1) = 612

Expand the equation:

n^2 + n = 612

Rearrange the equation to isolate the quadratic term:

n^2 + n - 612 = 0

Now, we can either factorize the quadratic equation or use the quadratic formula to find the values of n. Since this equation can be factored easily, let's go with that approach:

(n + 24)(n - 23) = 0

From here, we have two possible solutions:

n + 24 = 0 or n - 23 = 0

If we solve these equations separately:

1. n + 24 = 0
n = -24

2. n - 23 = 0
n = 23

Since the number of students cannot be negative, we can ignore the first solution. Therefore, there are 23 students in the second-grade class.