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Splitting Cow Heirs

In the reading of a rancher's will, his herd of cows was divided among his four surviving children:
  • His oldest daughter got one-half the herd
  • His oldest son got one-fourth the herd
  • His youngest son got one-fifth of the herd
  • And, his youngest daughter got the remaining 48 cows.
How many cows were in the rancher's original herd?


Hint: Try to solve it by drawing a picture (e.g. think long rectangle like a candy bar) and then shading in the respective parts that match the problem's information.

An algebraic equation will work, but the solution process is perhaps more interesting and revealing when done visually.


Solution Commentary: When you draw the rectangle, and shade in portions representing 1/2, 1/4, and 1/5, what fraction does the remaining 48 cows represent? You should get the fraction 1/20. Now, final answers come quickly as the fractions 1/2, 1/4. and 1/5 all convert easily to a common denominator of 20.

Feel free to check this solution using the algebraic equation 1/2 X + 1/4 X + 1/5 X + 48 = X, where X = the number of cows in original herd. In performing the algebraic manipulations, you should say deja vue.