In the 1870's, on a farm along the Ohio River, a girl was presented with three gifts: a rooster, a goose, and a duck. The duck had cost 20 cents. The rooster and the goose together cost twice as much as the duck. The goose and the duck together cost three times as much as the rooster. What is the cost of the goose and rooster alone?
d = 20
r+g = 2d
g+d = 3r
so,
r+g = 40
3r-g = 20
4r = 60
r = 15
g = 25
To find the cost of the goose and rooster, we can break down the given information and form equations based on the details provided.
Let's assign variables to represent the costs:
- Let's say the cost of the rooster is "r" cents.
- Let's say the cost of the goose is "g" cents.
According to the information given:
1) The duck cost 20 cents, so we can write the equation: duck = 20 (equation 1).
2) The rooster and the goose together cost twice as much as the duck, so we can write the equation: (rooster + goose) = 2 * duck (equation 2).
3) The goose and the duck together cost three times as much as the rooster, so we can write the equation: (goose + duck) = 3 * rooster (equation 3).
Now, we have a system of equations:
Equation 1: duck = 20
Equation 2: rooster + goose = 2 * duck
Equation 3: goose + duck = 3 * rooster
To solve the system of equations, we can substitute Equation 1 into Equations 2 and 3, replacing "duck" with 20.
Equation 2 becomes: rooster + goose = 2 * 20 -> rooster + goose = 40
Equation 3 becomes: goose + 20 = 3 * rooster -> goose = 3 * rooster - 20
Now, we can substitute the expression for "goose" from Equation 3 into Equation 2:
rooster + (3 * rooster - 20) = 40
4 * rooster - 20 = 40
4 * rooster = 60
rooster = 60 / 4
rooster = 15
Now, substitute the value of "rooster" back into Equation 3 to solve for "goose":
goose + 20 = 3 * 15
goose + 20 = 45
goose = 45 - 20
goose = 25
Therefore, the cost of the goose alone is 25 cents and the cost of the rooster alone is 15 cents.