Solution to Problem 3

answer:11

Solution:

let n equals the difference between Zoe’s and Chloe’s ages. The condition works when n has 9 factors. By inspection, 36 has 9 factors. Thus, Joey is 38 and will be 74 when Zoe is 37, so the answer is 7+4=11 .

解答:

假设n是田田和妈妈的年龄差,从题意得知n有9个因子。据观察得知36有9个因子。所以,爸爸今年38,当田田37岁的时候爸爸74岁。4+7=11.

Problem3

Joey and Chloe and their daughter Zoe all have the same birthday. Joey is 1 year older than Chloe, and Zoe is exactly 1 year old today. Today is the first of the 9 birthdays on which Chloe’s age will be an integral multiple of Zoe’s age. What will be the sum of the two digits of Joey’s age the next time his age is a multiple of Zoe’s age?

爸爸小朱、妈妈小敏和他们的女儿田田同一天生日。小朱比小敏大1岁,田田今天正好1岁。小敏有9个生日的年龄是田田年龄的整数倍,今天是第一个。请问:下一次小朱年龄是田田年龄整数倍的时候,父女俩的年龄和是多少?