Identifying Errors In Reasoning

Cows

Work Time

Cows

A farmer’s herd of cows is 20% smaller than it was the previous year. The farmer figured out that if each cow can increase milk production by 20%, then milk production will be the same as it was last year.

  • What mistake in reasoning about percents did the farmer make?
  • Using examples, explain why the farmer’s reasoning is incorrect.

Hint:

  • What amount would you take 20% of the first time you see the 20% in the problem?
  • What amount would you take 20% of the second time you see the 20%?