12 Arithmetic & Algebraic Problems- ANCIENT PROBLEM
Here is an example of the sort of "Breakfast Problem" propounded by
Metrodorus in 310 A.D.
Demochares has lived one-fourth of his life as a boy, one-fifth as a youth,
one-third as a man, and has spent thirteen years in his dotage. How old is
the gentleman?- FAMILY AGES
A man and his wife had three children, John, Ben, and Mary, and the dif-
ference between their parents' ages was the same as between John and Ben
and between Ben and Mary. The ages of John and Ben, multiplied together,
equalled the age of the father, and the ages of Ben and Mary multiplied to-
gether equalled the age of the mother. The combined ages of the family
amounted to ninety years. What was the age of each person?- MIKE'S AGE
"Pat O'Connor," said Colonel Crackham, "is now just one and one-third
times as old as he was when he built the pig sty under his drawing-room
window. Little Mike, who was forty months old when Pat built the sty,
is now two years more than half as old as Pat's wife, Biddy, was when Pat
built the sty, so that when little Mike is as old as Pat was when he built the
sty, their three ages combined will amount to just one hundred years. How
old is little Mike?"- THEIR AGES
Rackbrane said the other morning that a man on being asked the ages of
his two sons stated that eighteen more than the sum of their ages is double
the age of the elder, and six less than the difference of their ages is the age of
the younger. What are their ages?
- BROTHER AND SISTER
A boy on being asked the age of himself and of his sister replied:
"Three years ago I was seven times as old as my sister; two years ago I was