I need help answering my daughters 3th grade question.

Question

Heres the question we are having problems with....  Kira shares a plate of brownies with friends. Her friends each have 2 more brownies than Kira. There where 33 brownies in all. How many friends are there?

Answer 1

Use trial and error.

Suppose she has 1 friend. That means there will be 1 person with 2 extra brownies.
33 - 2 = 31
However, 31 is not divisible by 2 people (Kira and her friend).
Thus, this is not the answer.

Suppose she has 2 friends. That means that there will be 2 people with 2 extra brownies each.
33 - 2(2) = 29
However, 29 is not divisible by 3 people (Kira and her 2 friends).
Thus, this is also not hte answer.

Suppose she has 3 friends. That means that there will be 3 people with 2 extra brownies each.
33 - 3(2) = 27
However, 27 is not divisible by 4 people (Kira and her 3 friends).
Thus, this is also not hte answer.

Suppose she has 4 friends. That means that there will be 4 people with 2 extra brownies each.
33 - 4(2) = 25
Notice that 25 can be divided by 5, and you will get 5.
This means kira has 5 brownies.
5 + 2 = 7, which means each of her friends has 7 brownies.
Hence, Kira has 4 friends.

Answer 2

How do we not know if the answer is 6 friends with 5 brownies, while Kara has 3? 6 friends times 5 brownies each is 30. There are 3 left for Kara, which means her friends each have 2 more than she does.

Answer 3

well first you know that each friend had 2 brownies more than Kira and there are 33 brownies so count by 2 until you get to the closest number possible to 33 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32 and add 1 brownie for Kira so that equals 33 brownies now you add up all of the numbers you have counted and you get 16 so there are 16 friends

Answer 4

There are two answers

Add 2 brownies to the 33 to make it 35, so all girls ate the same number of brownies

35 has factors 5 and 7

if kira has 4 friends each girl eats 7 brownies 4 x7 = 28 plus the 5 kira ate (she ate 2 less thatn the others) = 33

it also works if kira has 6 friends that ate 5 brownies

This is a trick question and is not really fair for 3rd graders - someone should update the books

Answer 5

To confirm what others have said, the question can be written as an equation as follows:

C + N(C+2) = 33

Where C = #cookies that Kira gets, and N = number of friends.

There are 2 variables here (#Cookies and #Friends), and only one equation - there are infinitely many solutions to this, other than the constraint that the information available is that it can be assumed that both the #cookies and #friends are whole numbers - as others have pointed out.

The equation can be refactored to determine the number of friends based on the number of cookies, e.g.:

C + N(C+2) = 33
C + NC + 2N = 33
N(C + 2) = (33 - C)
N = (33 - C) / (C + 2)

e.g. for 3 cookies for Kira (C = 3)
N = (33 - 3) / (3 + 2)
= 30 / 5
= 6 Friends

for 5 cookies for Kira (C = 5)
N = (33 - 5) / (5 + 2)
= 28 / 7
= 4 Friends

Also note there is a whole-friend solution for all 33 cookies for Kira (C = 33) :-)
N = (33 - 33) / (33 + 2)
= 0 / 35
= 0 Friends!