Help with a math problem

Question

There are some three legged animals and some four legged animals altogether there are 101 legs, how much of each animal is there 

Answer 1

The way you have stated the problem there are multiple solutions. 

 

So so far all we know is that there are some animals with 3 legs we will say the number of them is x

 

x = number of 3 legs animals

 

and 4 legged animals. We will say the number of these is y

 

y = number of 4 legged animals 

 

therefore we have 3x + 4y = 101

 

we have only one equation and two unknowns. We need two equations to find a single solution. 

 

 We can find situations where values for x and y that will work

 

when x=3 and y=23 we have a solution 

 

3(3)+4(23)=101

 

also every time we increase x by 4 we will get another solution that works

 

x=7 and y=20

 

3(7)+4(20)=101

 

try some more and you will see that without the second equation we have many solutions 

 

good luck

Tom

Answer 2

x = number of 3-legged

y = number of 4-legged

 

3x + 4y = 101

 

Without more information (such as the total number of animals), there could be more than one solution.  However, you want both x and y to be positive integers.

 

y = (-3x + 101)/4

 

I suppose you can do trial and error runs until you find integer (x,y) pairs that satisfy this equation.