Question

Our class planned a holiday party for disadvantaged kids.some of us baked cookies for the party .on the day of the party we found we could divide the cookies into packets of two,three,four,five,or six and have just one cookie leftover in each case.if we divided them into packets of seven there would be no cookies left over.what is the least amount of cookies the class could have baked?

Answer 1

@phi

Answer 2

It's some multiple of 7 for sure.

Answer 3

Yea and the number is odd too

Answer 4

what are you studying?

Answer 5

This Is algebra

Answer 6

R u there

Answer 7

yes, but so far nothing is coming to mind.

Answer 8

if it's multiple choice, we could test each choice.
or if we *really* needed an answer, we can have a computer search for an answer.
But I think they want a clever way (which you have been studying??)
what have they been teaching that relates to this question?

Answer 9

We'll today we did a warm up on Order of operations

Answer 10

let me think about it.

Answer 11

Ok

Answer 12

301= 3*43 works

but I don't know a quick way to find it. Checking is easy:
301/2 = 150 r 1
301/3= 100 r 1
301/4 = 75 r 1
301/5 = 60 r 1
301/6= 50 r 1
301/7 = 43 r 0

Answer 13

Wait why use 3*43

Answer 14

@phi

Answer 15

oh, I meant 7*43 = 301

Answer 16

Where did you get 43 from

Answer 17

So you divided 7 to 43

Answer 18

But there must be a nicer way.

Answer 19

Oh wait what would I do next

Answer 20

what I tested were the multiples of 7:

0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105
and so on...

when I got to 301, it worked.

Answer 21

And to find out it worked you divided 301 to 7 and got 43 which is the least number of cookies

Answer 22

I should not have mentioned the 43 (that is the number of packets with 7 cookies in a packet)

the answer is 301 is the minimum number of cookies that they baked

Answer 23

Oh ok thanks so all I had to do was find the multiple of seven and since the other numbers had variables they didn't work so 301 is my final answr

Answer 24

It was a lot of work to do: check each multiple of 7 gives a remainder of 1 when divided by 2,3,4,5,6
I checked about 43 numbers (we could have eliminated the even numbers, so only checking about 20 something numbers.... but still a lot of work...

Answer 25

Oh thank you