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?
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.
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
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!!
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!
