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Brainwave 4

Fill the Tables

tables
Briony is on a bus trip, which stops for lunch at a cafe, which has tables for three or five people. There are 37 passengers on the bus. How can they be seated at these tables so that no single table has empty seats?
Find ANOTHER way they could be seated?

Is there any number of passengers (between 20 & 30) for which NO arrangement of people in 3’s and 5’s can be made?

Feature Solution

The feature solution for the problem came from Toby & Tahli and Alex & Liam from St Johns Cobar

Gold

Toby & Tahli
What did you have to find out?
For the first problem we had to find out how to make thirty seven passengers fit on tables of five and three with out having any single tables and seats left. For our second problem we had to do mainly the same as the first problem.

What materials did you use?
For the first problem we used our three times tables and five times tables and our maths book and a pen and a piece of paper.

How did you think? What strategies did you use? How did you solve this problem?
We wrote our three times tables and our five times tables out in our maths book. And then we got started by going down our three times tables and the five times tables and finding out what combinations equalled 37 when we added them together.

What answers did you come up with?
These are the answers that we came up with for the first problem 4x3=12 + 5x5=25 then 9x3=27 + 2x5=10

These are the answers for the second problem we got 20 people = 1x5=5 and 3x5=15 then 21 people = 3x5=15 and 2x3=6 then 22 people = 4x3=12 and 2x5=10 then 23 people = 1x3=3 and 4x5=20 then 24 people = 3x3=9 and 3x5=15 then 25 people = 5x3=15 and 2x5=10 then 26 people = 2x3=6 and 4x5=20 then 27 people = 4x3=12 and 3x5=15 then 28 people = 5x5=25 and 1x3=3 then 29 people = 4x5=20 and 3x3=9 then 30 people = 5x3=15 and 3x5=15 and they were our answers.

Alex & Liam
What did you have to find out?
We had to find out how to get to thirty seven by adding the three time tables and five time tables. Then we had to find out if you could go from twenty to thirty by using these tables. We found out that the numbers from twenty to thirty are all able to get by adding the three and five times tables together for the answers.

What materials did you use?
Paper, pens, math book, scrap paper, times tables.

How did you think? What strategies did you use? How did you solve this problem?
We thought hard and did all different combinations and found the right one. We used trial and error to find the answer. We used our knowledge to work out the tables and wrote down how to find out the answers. 20=3x5+1x5 21=2x3+3x5 22=4x3+2x5 23=9x3+2x5 24=3x3+3x5 25=3x5+2x5 26=1x5+7x3 27=3x4+5x3 28=1x3+5x5 29=1x5+3x8 30=0x5+10x3

What answers did you come up with?
We came up with the answers by getting an answer and checking it. We started with 5x4 and went up. The answer was 5x5+4x3 which equalled 37 which was our first answer. We kept on looking through and found 9x3+2x5 and it equalled 37. Then we found out 20-30 numbers could be used equally at the table. 20=3x5+1x5 21=2x3+3x5 22=4x3+2x5 23=9x3+2x5 24=3x3+3x5 25=3x5+2x5 26=1x5+7x3 27=3x4+5x3 28=1x3+5x5 29=1x5+3x8 30=0x5+10x3 and they were our answers.


Silver

Commendable contributors to the problem were:
Mitch, Noah & Abbey; Anna, Jayden & Jessie; Natalie & Maddie from Lord Howe Island CS
Winnie & Niamh from Abbotsford PS
Nathan & Diana from Homebush West PS
Kelsey; Sakshi-Sonam; Tamara & Alena; Eddy, Sam & Luke; Andrew & Joshfrom St Peter's Anglican Primary School

Bronze
Solutions were also sent in by:
Melissa & Grace; William & Lachlan; Joanne & Eric; Blake & Daniel; Trent & Jack; Jasmine & Kayla from St Peter's Anglican Primary School
Ashleigh & Emily; Nick, Connor & Braydon from St Johns Cobar
Jack & Hamish; James from Kempsey East PS
Annabelle, Jackson & Sam; Jenny & Rehan from Abbotsford PS