Thread: animals heads legs chickens

my 11yr old has been given some homework on ratios that i'm finding hard,
A farm has some chickens & some rabbits.
Altogether there are:
35 heads
94 legs
How many chickens are there?
and how many rabbits are there?
plus show your workings
Any help would be great

Originally Posted by lacourse

my 11yr old has been given some homework on ratios that i'm finding hard,
A farm has some chickens & some rabbits.
Altogether there are:
35 heads
94 legs
How many chickens are there?
and how many rabbits are there?
plus show your workings
Any help would be great

So it is about heads and legs.
Chicken has one head; rabbit has one head.
Chicken has two legs; rabbit has 4 legs.

Let c = number of chickens in there; and r = number of rabbits.

Re heads:
c*1 +r*1 = 35
c +r = 35 -------------(1)

Re legs:
c*2 +r*4 = 94
2c +4r = 94
Reduce that to its "lowest term", divide both sides by 2,
c +2r = 47 ------------(2)

One way to continue is by substitution.
From (1), c = 35-r
Substitute that into (2),
35-r +2r = 47
2r -r = 47 -35
r = 12
So, c = 35 -12 = 23

Therefore, there are 23 chickens and 12 rabbits in there. ------answer.

---------
Check.

Re heads,
c +r = 35
23 +12 =? 35
35 =? 35
Yes, so, OK.

Re legs,
2c +4r = 94
2*23 +4*12 =? 94
46 +48 =? 94
94 =? 94
Yes, so, OK.

Originally Posted by lacourse

my 11yr old has been given some homework on ratios that i'm finding hard,
A farm has some chickens & some rabbits.
Altogether there are:
35 heads
94 legs
How many chickens are there?
and how many rabbits are there?
plus show your workings
Any help would be great

As there are 35 heads we have 35 creatures altogether.
Counting two legs of each would account for a total of
70 legs, leaving 24 legs unaccounted for, which must
belong to 12 rabbits (to give each rabbit four legs)

So we have 12 rabbits and 23 chickens.

RonL

Thanks,
My daughter will be pleased