2200.61 – Holstein or Guernsey?

Three Guernsey cows and two Holstein cows give as much milk in four days as two Guernseys and four Holsteins give in three days. Which breed gives the most milk?

Solution

Let GG and HH be the daily milk production of one cow of each breed. Then we have

4(3G+2H)=3(2G+4H)12G+8H=6G+12H6G=4HG=2H3\begin{aligned}4 (3G + 2H) &= 3 (2G+4H) \\12 G + 8H &= 6G+12H \\6G &= 4H \\G &= \dfrac{2H}{3}\end{aligned}

so the Holstein breed produces more. A bit of Googling will show you that this is about right.