If there were 36 heads and 104 legs how many horses were their? How many riders were there?
r+h = 36
2r+4h = 104
Now just solve as usual.
From the first equation, we get:
r = 36 - h
Substituting this into the second equation, we get:
2(36 - h) + 4h = 104
Simplifying and solving for h, we get:
72 - 2h + 4h = 104
2h = 32
h = 16
So there were 16 horses. Substituting this back into the first equation, we get:
r + 16 = 36
r = 20
So there were 20 riders.
To determine the number of horses and riders, we can use the information given about the number of heads and legs.
Let's consider that each horse has one head and four legs, and each rider has one head but no legs.
Let's assume the number of horses to be "x" and the number of riders to be "y".
Based on the given information:
Number of heads: 36 (which includes both horses and riders)
Number of legs: 104
Taking into account the number of heads, we can write the equation:
x + y = 36 -- Equation 1
Taking into account the number of legs, we can write the equation:
4x + 0y = 104 -- Equation 2
Simplifying Equation 2, we get:
4x = 104
Dividing both sides of the equation by 4, we find:
x = 26
Substituting the value of x in Equation 1, we obtain:
26 + y = 36
Subtracting 26 from both sides of the equation, we have:
y = 10
So, there were 26 horses and 10 riders.
To determine the number of horses and riders, we can use a system of equations based on the given information.
Let's assume that each horse has one head and four legs, and each rider has one head and two legs.
Let H represent the number of horses, and R represent the number of riders.
Based on the given information, we have two equations:
1) The number of heads equation: H + R = 36 (Since the total number of heads is 36)
2) The number of legs equation: 4H + 2R = 104 (Since each horse has 4 legs and each rider has 2 legs)
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution:
From Equation 1), we can rearrange it to get R = 36 - H.
Now substitute this value of R into Equation 2):
4H + 2(36 - H) = 104
Simplify the equation:
4H + 72 - 2H = 104
Combine like terms:
2H = 32
Divide both sides by 2:
H = 16
Substitute the value of H back into Equation 1) to find R:
16 + R = 36
R = 36 - 16
R = 20
Therefore, there are 16 horses and 20 riders.