1550.15 – Rooster, Goose, Duck Prices

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. How much did the goose cost alone?

Solution

Let rr be the cost of the rooster, dd the cost of the duck, and gg the cost of the goose.

r+g=2d  ⟹  r+g=40r + g = 2d \implies r + g = 40

3r=g+d3r−g=20(3r−g)+(r+g)=20+404r=60r=15  ⟹  g=25\begin{align*}3r &= g + d \\3r - g &= 20 \\(3r - g) + (r + g) &= 20 + 40 \\4r &= 60 \\r &= 15 \implies g = 25\end{align*}

The goose cost 25 cents.