SOLUTION: There are 50 total ducks and cows in a field. 154 total legs can be counted. How many cows are there? How many ducks? I am going into 7th grade and not sure how to solve this.

Algebra ->  Human-and-algebraic-language -> SOLUTION: There are 50 total ducks and cows in a field. 154 total legs can be counted. How many cows are there? How many ducks? I am going into 7th grade and not sure how to solve this.       Log On


   

Question 892773: There are 50 total ducks and cows in a field. 154 total legs can be counted. How many cows are there? How many ducks?
I am going into 7th grade and not sure how to solve this.
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
let d = the number of ducks
c = the number of cows
( the number of ducks ) times ( 2 legs per duck )
+
( the number of cows ) times ( 4 legs per cow ) = 154
d*2 + c*4 = 154
We also know that the number of ducks plus the number of cows = 50
d + c = 50
We have two equations
d + c = 50 and d*2 + c*4 = 154. Let's rewrite the second equation
2d + 4c = 154
Using d + c = 50 let's solve for d
d + c = 50
add -c to each side
d = 50 -c
Substitute (50 - c) for d in 2d + 4c = 154
2(50 - c) + 4c = 154
100 -2c + 4c = 154
100 + 2c = 154
add -100 to each side
2c = 54
divide each side by 2
c = 27
Since d = 50 - c
d = 50 - 27 = 23
So we have 27 cows and 23 ducks
27(4 legs) + 23( 2 legs )
108 + 46 = 154 legs in total
27 cows and 23 ducks = 50 animals in the field