Problema Solution
Solve the following problem twice-
1. by substitution and by elimination
Farmer Red had 12 animals in his barnyard, all either cows or ducks. If the animals had a total of 38 legs, how many were cows and how many were ducks?
Answer provided by our tutors
Let
x = number of cows
y = number of ducks
number of cows + number of ducks = total number of animals
x + y =12
since every cow has 4 legs and every duck has 2 legs we have:
4*x + 2*y = 38
Lets solve the system
x + y =12
4*x + 2*y = 38
1) by substitution
from x + y =12 we can write x = 12 - y and substitute in the second equation
4*(12 - y) + 2*y = 38
48 - 4*y + 2*y = 38
-2*y = 38 - 48
-2*y = - 10 multiply both sides by (-1)
2*y = 10
y = 10/2
y = 5 ducks
x = 12 - y = 12 - 5 = 7 cows
2) by elimination
x + y =12
4*x + 2*y = 38
Multiply both sides of first equation by (-2) and add it to the second
-2x - 2*y = - 24
4*x + 2*y = 38
-------------------
-2x - 2y + 4x + 2y = - 24 + 38
-2x + 4x = 14
2x = 14
x = 7 cows
y = 12 - x = 17 - 7 = 5 ducks
There are 7 cows and 5 ducks in the barnyard.