Question Sam Loyd's Cyclopedia of Puzzles Answer
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Proposition: The ages of the three amount to 70 years and the father is just six times as old as the boy. When their combined ages amount to twice 70 years the father will be only twice as old as the boy. What is the age of the mother?

PUZZLES, AS they are termed, are always interesting, and possess a certain fascination for the young folks who are at all mathematically inclined. As a rule, they are extremely simple, but in he present case the data is so meager, and the proposition so different from what is expected, that the query actually appears startling.

It was sprung in the family circle the other day, and gave rise to a discussion which taxed the mathematical ingenuity of all present to the full limit.

One of the trio as represented in the picture was having a birthday anniversary, which aroused Master Tommy’s curiosity regarding their respective ages, and in response to his queries his father said:

“Now, Tommy, our three ages combined amount to just 70 years, and, as I am just six times as old as you are now, it may be said that when I am but twice as old as you, our three combined ages will be twice what they are at present. Now let me see if you can tell me how old is mother?”

Tommy, being bright at figures, readily solved the problem, but then he had the advantage of knowing his own age, and could guess pretty closely to the ages of the others. Our puzzlists, however, have merely the data regarding the comparative ages of the father and son, followed by the startling proposition as to “how old is mother?”

To tell Mother’s age experimentally, I would say that for every year of Tommy’s age his father must have six, viz.: if Tommy is 1 his father would be 6 so by adding four years to each, Tommy will be 5 and his father twice as much. So whatever age Tommy may be, as shown in the picture, he will be five times as old at the second stage, when their combined ages amount to 140. At first Tommy’s age plus six times his age, added to the mother’s equals 70. So the mother's age and seven times Tommy's age equals 70. Then Tommy gets four times as old, and as the father and mother both take on the same number of years, we find that the adding of twelve times Tommy’s first age has raised the combined ages of the three an extra seventy years. By dividing 70 by 12, therefore, we find that Tommy's age must have been 5 years and 10 months, the father six times as old, viz., 35 years, and the mother just 29 years and 2 months.


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