# Pheasants and Rabbits

#### MT Schull

##### New member
Kevin has pheasants and rabbits. He has a total of 42 heads and 138 legs. How many pheasants and rabbits does kevin have?

#### Denis

##### Senior Member
Have you at least tried?
Here's the 2 equations:
p + r = 42
2p + 4r = 138

If you can't solve, talk to your teacher.

#### Subhotosh Khan

##### Super Moderator
Staff member
MT Schull said:
Kevin has pheasants and rabbits. He has a total of 42 heads and 138 legs. How many pheasants and rabbits does kevin have?
Do you know algebra?

If you don't - then of course you cannot do the way Denis suggested.

In case you don't know algebra - then it is an "educated" guessing method.

Now you have 126 legs and 42 heads.

You are short of legs - 12 legs. To increase the number of legs - you need to exchange 1 pheasant for 1 rabbit. For increasing the no of rabbit by one (and decreasing number of pheasants) - you will gain 2 legs.

You need to increase 12 legs - so how many pheasants must you exchange (for rabbits)?

#### Denis

##### Senior Member
...and be careful when you pronounce "pheasant plucker" :wink:

#### MT Schull

##### New member
2p+4r=138. Solve for p and r.
Is this correct?
P=42-r
2(42-r)+4r=138
84-2r+4r=138
84+2r=138
2r=138-84
2r=54
r=27

2p+4(27)=138
2p+108=138
2p=138-108
2p=30
p=15

Kevin at 15 pheasants and 27 rabbits
15pheasant x2 legs=30 legs
27rabbitsx4 legs=108 legs
30+108=138

Thanks for the nudge. MT Schull

#### mmm4444bot

##### Super Moderator
Staff member
MT Schull said:
2p + 4r = 138

p = 42 - r

Is this correct? Yes

Include definitions for symbols p and r, when you turn in your work.

I see that you checked your solution. That's smart.

r = 27

2p + 4(27) = 138

Instead of going back to this equation, to determine p, here's another approach.

You already wrote a formula for p in terms of r (above). Now that you know r = 27, you can use that formula.

p = 42 - r

p = 42 - 27