Algebra Word Problem Help?
A farmer has pigs and chickens. She counted 140 eyes and 200 legs. How many pigs and how many chickens were there? Equation and answer please.
5 Responses
sam
08 Mar 2010
Eigengrau
08 Mar 2010
140 eyes = 70 total animals
p + c =70
200 legs = 4 per pig + 2 per chicken
4p + 2c = 200
Substitute, from equation (1), c = 70 – p
4p + 2(70 – p) = 200
4p + 140 – 2p = 200
2p = 200-140 = 60
p = 30
c = 40
S. R.
08 Mar 2010
70 = X(4) + Y(2) x times 4 plus Y times 2
DON’T EAT
08 Mar 2010
x= pigs
y= chickens
2x+2y=140
4x+2y=200
solve by elimination:
(-1)2x+(-1)2y=(-1)140
4x + 2y= 200
-2x+-2y=-140 add both equations together
2x=60 divide each side by 2
x=30 plug x value back into either of the equations
2(30)+2y=140
60+2y=140 subtract 60
2y=80 divide by 2
y=40
There were 30 pigs and 40 chickens, I’m pretty sure.
Brian R
08 Mar 2010
Both pigs and chickens have 2 eyes each right? So there has to be 70 animals (140/2 = 70). Now because there are 200 legs, you will need to write a formula to determine how many of the 70 are pigs and how many are chickens, and as you know, pigs have 4 legs and chickens have 2.
So using P for pigs and C for chickens, you have two equations and two unknowns, so you can solve the problem, the first equation is 4P+2C=200 (this is saying that for each pig there are 4 legs, and each chicken there are 2 legs, and total there are 200 legs). The second equation is P+C=70 (which we said above is how many total animals there are).
So you will solve the first equation by saying the number of Pigs has to be 70 minus the number of chickens, or, P=70-C. So substitute 70-C for the P in the first equation and you get:
4*(70-C)+2C=200
280-4C+2C=200
2C = 80
C = 40.
So you now know there are 40 Chickens, meaning there has to be 30 Pigs. To verify you will multiply 2*40 = 80, and 30*4 = 120, meaning you have 200 total legs and 140 total eyes, so it is correct.
30 pigs and 40 chickens