Word Problem

Question

If each student in a class sends a New Year greeting card to each of his classmates, a total of 870 cards will be sent. Find the number of students in the class 

Answer 1

each student sends one less card than the number of students altogether

if there are 3 students each student sends 2 cards for a total of 3*2=6 cards

if there are 4 students each student sends 3 cards for a total of 4*3=12 cards

each of 5 students sends 4 cards for a total of 5*4=20 cards

each of 6 students sends 5 cards for a total of 6*5=30 cards

and so on...

now you can see where the n*(n-1) comes from in Kenneth S.'s solution

you can solve the equation n(n-1)=870 to get the number of students

however, you can reason out the answer because each student sends out 1 less card then the number of students

therefore you must find 2 consecutive integers whose product is 870, and this is what you do when you solve the equation

so basically you factor 870 into a product of 2 consecutive integers and you have your answer

870=87*10=3*29*2*5=29*(3*2*5)=29*30

there are 30 students and each student sends out 29 cards to the other 29 students

Answer 2

How many pairings are there from n students?  nC2 = n(n-1)/2.

 

Each pairing involves two cards (e.g. A to B & B to A).  Therefore n(n-1) cards = 870.  Solve that!