There are 30 rabbits (4 legs) and ducks (2 legs) both together in a field counting their feet, there are 94 altogether. How many of each are there?

Question

Please show me every single working out please. Thanks :).

Answer 1

Hi Tuti!

This is a simple system of equations. First, you need to create equations that describe your problem. Let’s use r for rabbits and d for ducks. We’ll need one equation for the total number of animals, and one equation for the total number of legs. The system will look like this:

4r + 2d = 94 legs

r + d = 30 animals

In order to figure out how many of each animal there is, we want to use substitution. I can rewrite the second equation as r = 30 - d by subtracting d from both sides.

Now we substitute the new equation back into the top equation.

4r + 2d = 94 —> 4(30 - d) + 2d = 94

Using the distributive property, simplify the left.

120 - 4d + 2d = 94

Further simplify the left by combining like terms

120 - 2d = 94

Isolate d using inverse operation and moving the 120 and -2 to the other side

-2d = 94 - 120

-2d = -26

d = -26/-2

d = 13

This means there were 13 ducks. To figure out how many rabbits there were, we substitute 13 in for d and solve for r.

d + r = 30

13 + r = 30

Subtract 13 from both sides to isolate r.

r = 30 - 13

r = 17

There are 13 ducks and 17 rabbits in the field. I hope this helped!