I was playing Farmville again and my chicken coops and dairy farms disappeared. My farm was covered with animals. I noticed 226 legs and 70 heads. How many of each animal do I have on my farm?
If someone could please answer this, I would be so happy. I am not understanding this at all!
Please help!
Anonymous
This is an algebra problem.
Chickens have two legs (except for the rare amputee--beware hungry and impatient farmers!). Therefore, if x is the number of chickens, 2x = number of chicken legs.
Cows (or goats, if you like feta cheese...mmm) usually have four legs. Therefore, if y is the number of goats plus cows, then 4y = the number of goat and cow legs.
If there are 70 heads, then x + y = 70.
And if there are 226 legs, then 2x + 4y = 226.
Solve for one variable in the first equation: y = 70 - x.
Substitute for y in the second equation: 2x + 4(70 - x) = 226.
Or... 2x + 280 - 4x = 226.
-2x = -54.
x = 27.
Substitute this in the first equation:
27 + y = 70; y = 43.
Checking my work, I ask: does 2 times 27 plus 4 times 43 = 226?
2 * 27 = 54; 4 * 43 = 172. 54 + 172 does indeed equal 226.
Therefore, the number of chickens is 27, and the number of cows (or cows plus goats, or goats only, if you're just raising goats) is 43.
See how useful algebra can be?
Alvaro
26 chickens = 26 heads and 52 legs.
44 cows = 44 heads and 172 legs.
When you add them together you get 70 heads and 226 legs. :]