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*Shannon
StuckOnPeas
PeaNut 232,172
November 2005
Posts: 2,482
Layouts: 37
Loc: Along the Rockies
 |  Posted: 1/23/2013 8:35:13 PM
At the 2004 Olympics a sports commentator said: "USA is one of the 16 countries with the maximum allowed 3 runners. All together there are 103 runners representing 60 countries." How many countries have 2 runners?
Would anyone like to offer up their answer along with a lovely explanation?
Thank you!!! |
Contrary to popular belief, America is not a democracy (or a federation), it is a Chucktatorship. | |
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Zella
PeaFixture
PeaNut 434,965
August 2009
Posts: 3,319
Layouts: 5
Loc: Puget Sound
 | Posted: 1/23/2013 8:46:46 PM
It's actually pretty straightforward.
Number of runners is 103
Number of countries is 60
16 countries have 3 runners
16x3 = 48 runners
103-48 runners leaves 55
60 countries minus 16 that we know have 3 runners leaves 44 countries
If there are 55 runners, and 44 countries, you subtract the 44 from the 55 (one runner per country), and you have 11 runners remaining. Therefore, there must be 11 nations with two runners.
I hope that helps! |
Trying to live each day for itself
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pheestand
Ancient Ancestor of Pea
PeaNut 6,487
September 2000
Posts: 5,037
Layouts: 16
Loc: Livonia, MI USA
 | Posted: 1/23/2013 8:48:15 PM
60 countries total
16 have 3 runners each or 16 x 3 = 48 runners
remaining 44 countries with 55 total runners.
each country gets one runner, 55 runners, 1 each 44 countries - 11 runners left over to "double up".
so, 16 countries x 3 runners = 48 total runners
11 countries x 2 runners = 22 total runners
33 countries x 1 runners = 33 total runners
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isabel04
PeaNut
PeaNut 259,769
May 2006
Posts: 108
Layouts: 0
Loc: texas
| Posted: 1/23/2013 8:54:18 PM
16 countries with 3 runners = 48 runners. 103 runners total minus 48 runners = 55 runners left from the 44 remaining countries. 11 countries have 2 runners (22 runners) and 33 countries have 1 runner (33 runners). 48 runners + 22 runners + 33 runners = 103 runners
I think this is right. I just figured it out with the process of elimination. Hope this helps | |
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ScrampingMomof3
PeaAddict
PeaNut 154,784
June 2004
Posts: 1,116
Layouts: 0
Loc: Texas
 | Posted: 1/23/2013 8:55:58 PM
(16*3)=48 total runners from 16 countries
103-48=55 total runners from remaining 44 countries
x = number of countries with 1 runner
44-x = number of countries with 2 runners
x + 2(44-x) = 55 runners
x + 88 - 2x = 55
88 - x = 55
88 - 55 = x
33 = x
So,
x: 33 countries have 1 runner
44-x: 11 countries have 2 runners
16 countries with 3 runners: 48 runners
11 countries with 2 runners: 22 runners
33 countries with 1 runner: 33 runners
16+11+33= 60 countries
48+22+33= 103 runners
 subbing is keeping my brain alive! | |
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*Shannon
StuckOnPeas
PeaNut 232,172
November 2005
Posts: 2,482
Layouts: 37
Loc: Along the Rockies
| Posted: 1/23/2013 9:10:20 PM
Thank you, Zella, pheestand, isabel04, and Scramping Mom of 3 for answering.
I am almost there... math was not and is not my best subject. Each one of your explanations is helping me to understand. My daughter is also *almost* there. She's going to ask her teacher to explain it tomorrow.
I think I'm just missing a basic understanding of the algebra needed to set up and solve the problem.
THANK YOU!!
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Contrary to popular belief, America is not a democracy (or a federation), it is a Chucktatorship. | |
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ScrampingMomof3
PeaAddict
PeaNut 154,784
June 2004
Posts: 1,116
Layouts: 0
Loc: Texas
| Posted: 1/23/2013 9:18:18 PM
Do you and your daughter understand the way I set up the equation? | |
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*Shannon
StuckOnPeas
PeaNut 232,172
November 2005
Posts: 2,482
Layouts: 37
Loc: Along the Rockies
| Posted: 1/23/2013 9:24:00 PM
SM3 - I understand it as I look at it and go through it... I never would have been able to figure it out by myself. My brain doesn't do that. I think my daughter grasps the algebra better than I do. |
Contrary to popular belief, America is not a democracy (or a federation), it is a Chucktatorship. | |
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ScrampingMomof3
PeaAddict
PeaNut 154,784
June 2004
Posts: 1,116
Layouts: 0
Loc: Texas
| Posted: 1/23/2013 10:16:06 PM
OK. it may help if you look at it like this:
60 total countries
- 16 3 runner countries
=======================
44 countries left that sent 1 or 2 runners
so x = 1 set of countries; 44-x = other set of countries
48 runners from 16 countries that sent 3 runners each
x runners from x countries that sent 1 runner each
2(44-x) runners from 44-x countries that sent 2 runners each
So, 48 runners
+x runners
+2(44-x) runners
====================
103 total runners
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