Farmer Ben owns only cows and ducks. There are a total of 82 animals. One day, for fun, he counts that his animals have a total of 240 legs.
A. Write a single equation with ONE variable to model this situation. Define the variable.
x = the number of cows
80-x = the number of ducks
number legs number
of per of
animals animal legs
---------------------------------
cows x 4 4x
ducks 82-x 2 2(82-x)
---------------------------------
totals 82 240
The equation comes from the right
column:
4x + 2(82-x) = 240
B. Solve the equation to determine how
many of each animal Farmer Ben owns.
4x + 2(82-x) = 240
4x + 164 - 2x = 240
2x + 164 = 240
2x = 76
x = 38 cows
80-x = the number of ducks = 82-38 = 44 ducks.
Checking: The 38 cows have 38·4 = 152 legs.
The 44 ducks have 44·2 = 88 legs.
38+44 = 82 animals
152+88 = 240 legs.
That checks
Edwin
