l>Problem solving ContestProblem addressing ContestbyLacey Walker, Rory Statham, D"laney Bruneau, Ryan Flegg and Blair Jasper
Congratulations come the following students who entries were selected as winners in the recent middle level trouble solving contest. Our thanks to note Jensen the the mathematics department at the Melfort an extensive Collegiate because that judging the entries. Selections to be made ~ above the basis of accuracy, creativity, detail and also organization the the answers given.Problem 1In a polygon, a diagonal line is a line joining 2 non nearby vertices. A triangle has no diagonals. A quadrilateral has actually 2 diagonals. A pentagon has 5 diagonals. How plenty of diagonals would be in a 15 sided polygon?Winner - Lacey WalkerGrade 6 , Star City SchoolLacey"s prize - The first thing i did to fix this trouble was an alert a sample in the polygons that had an odd variety of sides. A triangle has 0 diagonals, a pentagon has 5 diagonals, a 7 face polygon has 14 diagonals, a 9 sided polygon has 27 diagonals. ( check out diagrams ). This is the sample that ns discovered: 3 sided:3 x 0 = 0
5 sided:5 x 1 = 5
7 sided:7 x 2 = 14
9 sided:9 x 3 = 27
11 sided:11 x 4 = 44
13 sided:13 x 5 = 65
15 sided:15 x 6 = 90
Therefore, there are 90 diagonals in a 15 face polygon.Note indigenous The Centralizer: over there is a breakthrough of the expression behind Lacey"s sample in the Quandaries and Queries ar of Math central in a keep in mind titled Diaginals in a Polygon.Problem 2Paul areas 7 bags the marbles ~ above a table. The second bag has 2 much more marbles 보다 the first bag. The third bag has actually 4 more marbles 보다 the second bag. The 4th bag has 6 more marbles 보다 the 3rd bag and so on. The total variety of marbles in all seven bags is 231. How numerous marbles are there in each bag?Winner - Rory StathamGrade 7 , Star City SchoolRory"s prize - very first of all, to figure this inquiry I divided 7 into 231 and got 33. Since I got 33, ns knew that there couldn"t it is in any more than 33 marbles in the an initial bag. So I began with a smaller sized number prefer 14 in the first bag. I offered a chart and also the guess and also check an approach to find what numbers would job-related to obtain 231. Mine answers room 17, 19, 23, 29, 37, 47 and 59. (see chart)1st2nd3rd4th5th6th7th totalcheck
14162026344456 210no
151721273545 57217no
161822283646 58224no
171923293747 59231yes
Problem 5A sample is make of alternate red and black disks. The an initial row has actually only one disk, the second row has actually three disks, the third row has five disks and so on. Each heat begins and ends v a black disk. How numerous red disks space there in the an initial to fiftieth rows inclusive.Winner - D"laney BruneauGrade 6 , Star City SchoolD"laney"s prize - an initial of all, I attracted a snapshot to number out the question.

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From the snapshot I observed that heat 1 has 0 red disks, row 2 has actually 1 red disk, row 3 has actually 2 red disks, row 4 has 3 red disks. I think this pattern will proceed until heat 50 has actually 49 red disks. Now I have to add all the number from 1 come 49 to get the total. I added all the numbers on my calculator to gain 1225, which i think is the answer. Then ns remembered finding out at the start of class 6 exactly how to add a bunch of number in a row, favor all the number from 1 to 49. ...................1 + 2 + 3 + 4 + 5 + ..........+ 24 + 25 + 26 +..........45 + 46 + 47 + 48 + 49I added the 1 and 49 to obtain 50. I added the 2 and also 48 to obtain 50. I added the 3 and 47 to get 50. The including went on like this until in the middle I included the 24 and 26 to gain 50. Lastly I gained to 25 i m sorry didn"t have actually a partner. Now, to get the answer I recognize that there room 24 bag of 50 and the 25 through itself. Therefore the price is 24 x 50 = 1200. Climate 1200 + 25 = 1225.Problem 6Ryan has been collecting coins for his yearly Telemiracle donation. His donation that $7.30 is made up of nickels, dimes and quarters. If he has 47 coins in total, how many of each sort of coin did that have? Is there much more than one equipment to the problem?Winner - Ryan FleggGrade 7 , Star City SchoolRyan"s price - To discover the answer come this question I made a chart and put in the number of nickels, dimes and also quarters that I believed would do $7.30. I guessed 17 nickels, 20 dimes, and also 10 quarters yet that was as well low ($5.35), for this reason I added 3 much more nickels, left the dimes the same and took far 3 quarters yet my prize got even lower ($4.75). For this reason using usual sense, i jacked up the soldier by 13 since they have better value, left the dimes the same and also took far 13 nickels. Now my price of $7.35 was only 5 cents also high. So lastly I took away 1 dime and included 1 nickel and also this provided me an also $7.30. The number of coins that functions is 8 nickels, 19 dimes and 20 quartersNickelsDimesQuartersTotal
172010$5.35
20207$4.75
72020$7.35
81920$7.30
Problem 7
Sue, the owner of rectangular Catering solutions Inc. Is trying to determine the best means of seating client in her cafeteria. The tables that space used deserve to sit 10 people; four along every side and also one at each end. She decides to sign up with the tables together end to end. If her cafeteria has enough length because that 10 tables to be placed end to end to do one row, and also enough width for 5 of these rows, how countless customers can be sit at one time?Winner - Rory StathamGrade 7 , Star City SchoolRory"s price - I supplied a chart to help me recognize this problem. First I witnessed that once tables are put end to end they will only seat 8 people but the ones in ~ each finish would seat 9 people. If there room 10 tables in a row then there will certainly be 10 x 8 = 80 human being along the sides. Currently I can multiply through 5 since there are 5 rows to acquire 5 x 80 = 400. Currently I can add on 10 because there are 5 along the front of each row and also 5 follow me the end of each row. Therefore my last answer will be: 10 x 8 x 5 + 10 = 410 people.
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Problem 8Beth is a pedestrian who have the right to walk in ~ a pace of 5 kilometres per hour. Lanny is a jogger who runs in ~ a pace of 8 km per hour. Beth is an early riser and Lanny likes to sleep in. Top top a beautiful feather day, Beth awakens in ~ 7 a.m. And begins she walk. Three hrs later, at 10 a.m. Lanny finally awakens and begins to jog, following the same route they always use. Assuming castle love to practice at what time will Lanny record up to Beth? Plot ordered pairs of (time, distance) to highlight the answer.Winner - Blair JasperGrade 9, F.W. Johnson CollegiateRegina, SaskatchewanLanny will catch up to Beth in ~ 15:00 hours.

See more: What Numbers Are Divisible By 9, Numbers Divisible By 9 And 10

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