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10/06/2010 08:50:22 PM · #1 |
Can someone help us figure out this:
14. The total number of horses and people at the riding academy for the Friday session was 39. The total number of legs at the academy that day was 124. How many people were at the riding academy that Friday?
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10/06/2010 08:54:13 PM · #2 |
x = people
y = horses
x + y = 39
y = 39 - x
2x + 4y = 124
Substitute from here. |
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10/06/2010 08:54:54 PM · #3 |
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10/06/2010 08:56:11 PM · #4 |
Originally posted by neophyte:
23 horses 16 riders |
Show your work. -2pts
:) |
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10/06/2010 08:56:15 PM · #5 |
n = 39
x = 124
2a + 4b = 124
a + b = 39
And go. |
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10/06/2010 08:56:46 PM · #6 |
| Damn - i'm coming here for help from now on. |
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10/06/2010 08:58:36 PM · #7 |
I did t differently 39x 4 = 156
156-124 = 32/2= 16 riders
39-16=23 |
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10/06/2010 08:58:51 PM · #8 |
All of them...
Let's assume all of them were people. 2x39=78 Not enough legs.
Let's assume all were horses. 4x39=156 Too many legs.
Now we have an area to work in. What ratio will give us the proper number. Since horses have more legs it might be easier to figure from that direction...4x10=40 horse legs, leaving 84. 84/2=42 people, once again too many. Keep working it that way and soon you'll find an answer to your mystery.
Sorry, I didn't realize they were already teaching algebra in 6th grade.
Message edited by author 2010-10-06 21:01:35. |
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10/06/2010 09:08:50 PM · #9 |
| Thanks...my daughter is working it her way...I'll keep you posted and post what we come up with. |
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10/06/2010 09:19:24 PM · #10 |
This is what my daughter came up with. However, it looks like the book uses algebra but I can't find the exact problem in the book. We are working from a sample test.
Thanks
Originally posted by neophyte:
I did t differently 39x 4 = 156
156-124 = 32/2= 16 riders
39-16=23 |
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10/06/2010 11:00:56 PM · #11 |
That's a very elegant approach neophyte. Nice :-)
The class is probably teaching a method called "simultaneous equations" (at least it was in my youth in the UK) which is what alfresco laid out for you. I'm just going to take it the next step.
I used h for # of horses and p for # of people. Then what we are told can be expressed in the following two equations.
h + p = 39 (1)
4h + 2p = 124 (2)
Rearrange (1) to p = 39 - h
Substitute (39 - h ) instead p in (2) and you get 4h + 2(39-h) = 124
Rearrange that to 4h + 78 -2h = 124
Collect the similar terms and you get 2h = 124 - 78, which is 2h = 46, or h=23. So there are 23 horses
Substitute 23 for h back in (1) and you get 23 + p = 39. which is p = 39-23, or p = 16, so there are 16 people.
This is a much longer way to get to what Neophyte showed. Just to demonstrate the approach that might be being taught in the class
Edited to correct where I wrote horses for people in the last line!!! Oh well, I was having such fun doing it!!
Message edited by author 2010-10-07 07:23:33. |
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10/07/2010 03:11:05 AM · #12 |
| I really struggled with simultaneous equations when I was at school. What age group is 6th grade? |
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10/07/2010 03:46:01 AM · #13 |
Originally posted by SaraR:
I really struggled with simultaneous equations when I was at school. What age group is 6th grade? |
12 |
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10/07/2010 04:14:10 AM · #14 |
| I loved all this stuff at school ... sad I know ;) |
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10/07/2010 05:13:43 AM · #15 |
| Actually, there were 17 people. Two of them were pirates. |
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10/07/2010 06:24:44 AM · #16 |
I love algebra! I had to sit down and work it out last night, even though someone had already solved it.
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10/07/2010 06:30:36 AM · #17 |
| its a trick question, there is one three legged horse, so its impossible to solve. |
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10/07/2010 06:32:41 AM · #18 |
Originally posted by vawendy:
I love algebra! I had to sit down and work it out last night, even though someone had already solved it. |
you should try differential equations, once you get pass all the proofs and crap and actually solve problems, those are fun. |
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10/07/2010 07:43:09 AM · #19 |
| Unfortunately for us in America, in China this is 4th grade math. |
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10/07/2010 09:00:32 AM · #20 |
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10/07/2010 09:24:24 AM · #21 |
Originally posted by photodude:
Unfortunately for us in America, in China this is 4th grade math. |
Actually I think that America is the only place which studies math...
In Europe , it is Maths, or some french/german/italian etc equivalent. In China it is 'Shùxué' (phonetically)
;o)
Message edited by author 2010-10-07 09:24:54. |
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10/07/2010 09:58:56 AM · #22 |
Originally posted by PennyClick:
That's a very elegant approach neophyte. Nice :-)
The class is probably teaching a method called "simultaneous equations" (at least it was in my youth in the UK) which is what alfresco laid out for you. I'm just going to take it the next step.
I used h for # of horses and p for # of people. Then what we are told can be expressed in the following two equations.
h + p = 39 (1)
4h + 2p = 124 (2)
Rearrange (1) to p = 39 - h
Substitute (39 - h ) instead p in (2) and you get 4h + 2(39-h) = 124
Rearrange that to 4h + 78 -2h = 124
Collect the similar terms and you get 2h = 124 - 78, which is 2h = 46, or h=23. So there are 23 horses
Substitute 23 for h back in (1) and you get 23 + p = 39. which is p = 39-23, or p = 16, so there are 16 people.
This is a much longer way to get to what Neophyte showed. Just to demonstrate the approach that might be being taught in the class
Edited to correct where I wrote horses for people in the last line!!! Oh well, I was having such fun doing it!! |
I never saw this a double variable equation. Thanks for explaining! |
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10/07/2010 10:07:36 AM · #23 |
Originally posted by Strikeslip:
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Well that's not a very nice way for the rider to treat his horse.
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10/07/2010 10:33:38 AM · #24 |
| Also, he's using one of the pirates legs to beat him. That'll really mess the equations up. |
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10/07/2010 11:13:33 AM · #25 |
Originally posted by mike_311:
Originally posted by vawendy:
I love algebra! I had to sit down and work it out last night, even though someone had already solved it. |
you should try differential equations, once you get pass all the proofs and crap and actually solve problems, those are fun. |
I loved diffy q's!! That was my favorite math class!
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