Yahoo Answers: Answers and Comments for Help me with this question: On school camp a group of children went horse riding. Each child had a horse. Half decided to ride their horse while the other half decided to walk beside it. If there were 70 legs on the ground, how many children were there? [Mathematics]
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From Anonymous
enSG
Wed, 22 May 2019 10:07:00 +0000
3
Yahoo Answers: Answers and Comments for Help me with this question: On school camp a group of children went horse riding. Each child had a horse. Half decided to ride their horse while the other half decided to walk beside it. If there were 70 legs on the ground, how many children were there? [Mathematics]
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From Puzzling: INTUITIVE METHOD:
Half are riding on the hors...
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Wed, 22 May 2019 13:51:57 +0000
INTUITIVE METHOD:
Half are riding on the horse (4 legs) and half are walking by the horse (6 legs), so the average number of legs per child (with horse) is 5 legs.
70 / 5 = 14 children
ALGEBRAIC METHOD 1:
Let x be the total number of children.
Half (x/2) are riding > 4 legs
4(x/2) > 2x
Half (x/2) are walking > 6 legs
6(x/2) > 3x
Together that's 70 legs:
2x + 3x = 70
5x = 70
x = 70/5
x = 14
ALGEBRAIC METHOD 2:
Let x be the total number of children.
They each have a horse (4 legs), so that would be 4x legs for the horses.
Half of them are walking, so that would be (½x)*2 = x legs for the children that are walking.
Together that's 70 legs:
4x + 1x = 70
5x = 70
x = 70/5
x = 14
Answer:
14 children (with 14 horses, 7 are walking next to them).

From emma: that sounds so weird “70 legs on the ground” l...
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Thu, 23 May 2019 00:10:54 +0000
that sounds so weird “70 legs on the ground” lol whoever is writing these word problems really running out of ideas

From Φ² = Φ+1: Hint: For every pair of children (one riding t...
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Wed, 22 May 2019 10:14:00 +0000
Hint: For every pair of children (one riding their horse, one walking their horse) they are standing on 10 legs.
If there are 70 legs then ...

From Krishnamurthy: 14
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Wed, 22 May 2019 13:36:00 +0000
14

From Jeff Aaron: Continuing Ian's logic, since there were 7...
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Wed, 22 May 2019 13:19:04 +0000
Continuing Ian's logic, since there were 7 pairs of children, that's 7 * 2 = 14 children.

From Ian H: The number deciding to ride was equal to the n...
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Wed, 22 May 2019 12:03:35 +0000
The number deciding to ride was equal to the number that decided to walk.
The horses 4 legs and the 6 legs of horse + walking child means that there are 10 legs for every 2 children, (first observed by Φ² = Φ+1)
Since were 7 lots of 10 legs on the ground, there were 7 pairs of children
So that makes .......... ?

From Amy: number of horses = number of children
Number ...
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Wed, 22 May 2019 10:50:25 +0000
number of horses = number of children
Number of legs on the ground = (4 x number of horses) + (2 x 1/2 x number of children)

From JSG: Let x = number of kids.
Half are riding a hor...
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Thu, 23 May 2019 22:33:16 +0000
Let x = number of kids.
Half are riding a horse so there are 4 legs on the ground, and 4(x/2) or 2x is the number of legs on the ground.
Half are walking beside a horse so there are 6 legs on the ground, so 6(x/2) or 3x is the number of legs on the ground.
The total number of legs on the ground is 70, so:
2x + 3x = 70
5x = 70
x = 14
There are 14 kids.
Let's check this.
Each kid has 2 legs, so 14 kids have 28 legs total.
Half of the kids, which is 7, have 14 legs total.
Each kid has a horse and each horse has 4 legs.
For each kid on a horse there are 4 legs total on the ground.
For each kid walking besides a horse there are 6 legs total on the ground.
7 kids are on a horse so there are 28 legs total on the ground.
The other 7 kids are besides a horse so there are 42 legs total on the ground.
28 legs + 42 legs = 70 legs total.
There are 14 kids.