During a recent census, a man told the census taker that he had three children. When asked their ages, he replied, "The product of their ages is 72. The sum of their ages is the same as my house number." The census taker ran to the door and looked at the house number. "I still can't tell," she complained. The man replied, "Oh that's right, I forgot to tell you that the oldest one likes chocolate pudding." The census taker promptly wrote down the ages of the 3 children. How old are they?

Question

Mathematics

Ruth Wang

26 September, 16:34

During a recent census, a man told the census taker that he had three children. When asked their ages, he replied, "The product of their ages is 72. The sum of their ages is the same as my house number." The census taker ran to the door and looked at the house number. "I still can't tell," she complained. The man replied, "Oh that's right, I forgot to tell you that the oldest one likes chocolate pudding." The census taker promptly wrote down the ages of the 3 children. How old are they?

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Answers (2)

Know the Answer?

Camille · Answer 1

Answer: Their ages are 2 years, 3 years and 12 years old respectively.

Step-by-step explanation: The first clue given to the census officer is that the product of their ages equals 72. So if their ages are a, b and c, then

a x b x c = 72

In other words, we need to find three factors whose product equals 72.

The prime factors of 72 are

2 x 2 x 2 x 3 x 3 = 72

However, he also states that the sum of their ages is the same as his house number. The oldest one likes chocolate pudding. That is food not suitable for children below a certain age.

The AAP (American Academy of Pediatrics) recommends that children under 12 shouldn't eat or drink caffeine containing foods or drinks, even things like chocolate pudding.

So we already know that the oldest child is 12 years old. If the product of their ages is 72, then the other two children can be calculated as 72 divided by 12 which equals 6.

The factors of 6 are 2 and 3. That eventually tells us the ages of all three children, that is, their ages are 2, 3 and 12 years respectively.

Julie Weaver · Answer 2

They are 3, 3 and 8 years old

Step-by-step explanation:

If the product of their ages is 72, then the possibilities are:

Ages: Sum of ages:

1 1 72 74

1 2 36 39

1 3 24 28

1 4 18 23

1 6 12 19

1 8 9 18

2 2 18 22

2 3 12 17

2 4 9 15

2 6 6 14

3 3 8 14

3 4 6 13

The sum of ages are given. The possible answers are 3 6 6 and 3 3 8 (the only results with the same sum), otherwise the census taker would know the ages after looking the house number.

"the oldest one likes chocolate pudding" means that there is only one oldest child, this eliminate the option 3 6 6.