Make Herbert’s share 12 in both: 4 to 3 becomes 12 to 9, and 6 to 7 becomes 12 to 14. That’s 35 nuts a round, 770 is 22 rounds, so they get 22 × 12, 22 × 9 and 22 × 14.
Three boys share a bag of 770 nuts. Whenever Herbert takes four, Robert takes three, and whenever Herbert takes six, Christopher takes seven. How many nuts does each boy end up with?
Give me a hintThe hint
Put both clues in terms of the same number of Herbert’s nuts.
Reveal the answerHide the answer
Herbert 264, Robert 198, Christopher 308
Source: Henry Dudeney, Amusements in Mathematics, 1917, No. 50