Elementary POW, April 14-18, 1997
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There is a joke among radio broadcasters about the number of people who start leaving Dodger Stadium in the seventh inning of baseball games. One evening, during a particularly boring game in which the Dodgers were trailing by six runs after six innings, the fans began to leave at a record pace. After the first out in the top of the seventh inning, 100 fans left. After the second out, 150 fans left. After the third out, 200 fans left. The pattern continued in this way, with 50 more fans leaving after each out than had left after the previous out. The ridiculous thing was, the Dodgers tied up the game in the bottom of the ninth inning, and people still kept leaving early.The game lasted ten innings (The Dodgers lost anyway), and the pattern continued through the bottom of the tenth inning. How many fans left early?
Problem courtesy of Key Curriculum Press, Problem Solving Strategies, Crossing the River with Dogs.This week's mentors are Matt Gehrett and his students from Ridgeview High School in Bakersfield, California, who write:There were many responses to this week's problem.
The correct answer is 14,950 fans left early.
Daniel Kauffman
5th grade
Mrs. Harclerode
Lowther South Intermediate School
215 West 6th
Emporia,Kansas 66801
jharcler @usd253.kansas.netMy solution is 14,950
Dear Mrs. Carver,
We think we have came to the conclusion for your problem. We think that the answer is 14,950 people left early. We figured it out by continuing the pattern for each inning. Then we figured out how many people left each inning. Then we added up how many people left each early for each inning. For the tenth inning there were only five outs instead of six beacuse if they left after the sixth out they would be leaving at the end of the game not early.
Evan Sultanik
We think 14,950 people left the game early.
HOW MANY PEOPLE LEFT DURING THE INNINGS OUTS 7th inning 8th inning 9th inning 10th inning 1 100 400 700 1000 2 150 450 750 1050 3 200 500 800 1100 4 250 550 850 1150 5 300 600 900 1200 6 350 650 950 1250To find out the sum of all the numbers, we added the highest and lowest numbers (100 and 1250 which equal 1350). We multiplied that by 12 which is how many pairs of 1350 we could make with all the numbers. We got 16,200. Then we realized we had to subtract 1250 from the sum because the game is over at the end of the 10th inning, so those people would not have left EARLY. That left 14,950 people who left the game early.Bast,Leslie Faylor, Zach Seibert, Jessi Soler,Andrew Staffaroni, grade 3; Ashoke Khanwalkar, Adam Leposa, Mike Twardzik, grade 4; Doug Heather Comerci, Andrew Dang, Gordon Faylor, Sam Henderson, grade 5
Brianna Sosa
Fifth Grade
Mrs. Harclerode
Lowther South Intermediate School
215 West 6th
Emporia, Kansas, 66801
jharcler@usd253.kansas.netMy solution was 14,950 people would leave early by the end of the game. If 50 people would leave early every out, then I didn't need to count the last out because that was the end of the game. It adds up to 14,950 people leaving tthe Dodger Stadium early.
From: Mrs. Hanley's 3rd Grade Math Group (Emily, Jamie, Katie, Alicia, Tim, Andrew, John, Jeff, Alex, and Dan) from Gilead Hill Elementary School in Hebron, CT.
(e-mail= LHanley303@aol.com)Our class figured out that 14,950 fans left early from the baseball game.
We used a diagram to show how many fans left after each out, and then we added up all the numbers. We agreed that there were 6 outs per inning, 3 for each team.
7th inning - Out 1 100 fans 8th inning - Out 1 400 fans Out 2 150 Out 2 450 Out 3 200 Out 3 500 Out 4 250 Out 4 550 Out 5 300 Out 5 600 Out 6 350 Out 6 650 ----- ----- 1,350 fans left in 7th 3,150 fans left in 8th 9th inning - Out 1 700 10th inning - Out 1 1000 Out 2 750 Out 2 1050 Out 3 800 Out 3 1100 Out 4 850 Out 4 1150 Out 5 900 Out 5 1200 Out 6 950 ----- ------ 4,950 fans left in 9th5,500 fans left in 10th before the last out. We did not count the 6th out because everyone left after the 6th out because it was the end of the game.Finally, we added the total for each inning.
1350+3150+4950+5500= 14,950 total fans who left before the end of the game.From: David Gebauer, Scott Stewart, Bill Armstrong, and Brian Suessine
Donelson Hills School, Waterford, Michigan
mw11owat@moa.net
Teacher: Mr. Walton
Grade 5We think the answer is 14,950 fans left early.We started with 100 fans leaving after the first out of the seventh inning and kept on adding 50 more fans leaving each out.There are six outs in each inning.We knew we had to stop at the fifth out in the tenth inning because if you wait until the sixth out of the tenth inning it will be over.We added all the fans that left early together and got a total of 14,950 fans left early.
My answer was 14,950 fans left the crowd from the Top 7th inning to the bottom 10 inning second out. I just used a picture to help me solve the problem. In column form I put how many people left after each out until the 2nd out of the 10th inning. I did notice that after each 1/2 inning, that the total people that left was 450 less than the next 1/2 inning.
Dustin Brondyke, Age 8, Home School
Three Oaks Elementary School
Three Oaks MI
Teacher: Ringler/Carter
Grade: 5
E-mail: jringler@remc11.k12.mi.us
Student: AlisonFirst I knew that every out in visitors and home 50 fans left it did this from the 7th inning to the end of the 10th inning. (There was 1 extra inning.) I knew that in the 7th inning, 100 fans left the first out. The 2nd 150 fans left. The 3rd 200 and so on adding 50 each time. I came up with the following. In the 6 outs in the 7th inning altogether, 1350 fans left. In the 8th inning out of the 6 outs altogether 3150 fans left. In the 6 outs in the 9th inning altogether, 4950 fans left. Out of the 6 outs in the 10th inning altogether 5500 fans left. Then I added up all the numbers of fans in all the innings 7,8,9, and 10 and got 14,950 fans. I found this out by making a chart and logical reasoning. I made a chart for every inning. I add the 50 to each number. That is how I got my answer.
Name: Joseph Cross
Grade: Third
Teacher: Ms. Broach
School: Maret School
City: Washington, DCSolution:
The answer is 14,950 people left early. It would be 15,000 but the question is how many left early meaning before the last out of the game.
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