A farmer has some rabbits and some cages. When he puts two rabbits in each cage, there are two rabbits Left over.When he puts 3 rabbits in each cage, there are 16 extra cages, but no rabbits left over. How many rabbits and how many cages? (Write an equation for total rabbits and one for total cages. If you can't solve with an equation, try another method)
I need help with finding the two equations?
To find the two equations, let's assign variables to the number of rabbits and cages.
Let's say the number of rabbits is represented by the variable 'r' and the number of cages is represented by the variable 'c'.
First, let's form an equation based on the information that when the farmer puts two rabbits in each cage, there are 2 rabbits left over.
When the farmer puts two rabbits in each cage, the number of cages needed would be 'r/2' (because each cage holds 2 rabbits) and there are 2 rabbits left over, so our first equation would be:
r = 2(c + 1)
The "+1" represents the two extra rabbits left over.
Next, let's form an equation based on the information that when the farmer puts 3 rabbits in each cage, there are 16 extra cages but no rabbits left over.
When the farmer puts 3 rabbits in each cage, the number of cages needed would be 'r/3' (because each cage holds 3 rabbits) and there are no rabbits left over (indicating total division), so our second equation would be:
c = (r/3) - 16
Here, we subtract 16 from the number of cages needed because there are 16 extra cages.
So, we have two equations:
1) r = 2(c + 1)
2) c = (r/3) - 16
Now, you can use these equations to solve for the number of rabbits and cages.