Puzzling Ages :

Three boys were given a bag of nuts as a Christmas present,

and it was agreed that they should be divided in proportion to their ages,

which together amounted to 17½ years. Now the bag contained 770 nuts,

and as often as Herbert took four Robert took three, and as often

as Herbert took six Christopher took seven.

How many nuts each had, and what were the boys' respective ages?

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Puzzling Ages : ANSWER

When Herbert takes twelve, Robert and Christopher will take nine and fourteen respectively,

and that they will have together taken thirty-five nuts. As 35 is contained in 770 twenty-two times,

we have merely to multiply 12, 9, and 14 by 22 to discover that Herbert's share was 264,

Robert's 198, and Christopher's 308. Then, as the total of their ages is 17½ years

or half the sum of 12, 9, and 14, their respective ages must be 6, 4½, and 7 years.