A census-taker rings Mr. Manning's bell and asks how many children he has.
"Three daughters," he replies.
"And how old are they, in whole numbers?" asks the census-taker.
"Well, I'll tell you this:the product of their ages is 72, and the sum of their ages is my house number."
"But that isn't enough information!" complains the census-taker.
"Okay, my oldest daughter(in years)likes chocolate milk," replies Mr. Manning.
With that, the census-taker nods and writes down the three ages.
How old are the Manning girls, and how did the census-taker figure it out?Include a full explanation! *My teacher said "But that isn't enough information!" complains the census-taker. was a big hint but i don't get it please help
I need help please ASAP
i don't know :P
To solve this problem, we need to use the information provided by Mr. Manning and the response from the census-taker. Let's break down the information step by step:
1. Mr. Manning says he has three daughters.
2. The product of their ages is 72.
3. The sum of their ages is the house number.
4. Mr. Manning reveals that his oldest daughter likes chocolate milk.
Using this information, we can start by finding all the possible combinations of three whole numbers that multiply to 72. We can do this by listing all the factors of 72:
1 x 72 = 72
2 x 36 = 72
3 x 24 = 72
4 x 18 = 72
6 x 12 = 72
8 x 9 = 72
Since the census-taker initially says, "That isn't enough information!" but later figures out the ages, we can deduce that the product of the ages (72) has multiple combinations that match the sums of the ages, indicating unique possibilities.
To figure out the exact ages, we need to consider the additional clue given by Mr. Manning about his oldest daughter liking chocolate milk. Since the census-taker was able to determine the ages based on this information, it implies that there must be a unique oldest daughter.
To find the unique oldest daughter, we look for combinations where her age cannot be shared with any of the other daughters. Let's analyze the combinations:
1 x 72 = 72 (Sum = 1 + 72 = 73)
2 x 36 = 72 (Sum = 2 + 36 = 38)
3 x 24 = 72 (Sum = 3 + 24 = 27)
4 x 18 = 72 (Sum = 4 + 18 = 22)
6 x 12 = 72 (Sum = 6 + 12 = 18)
8 x 9 = 72 (Sum = 8 + 9 = 17)
Looking at the sums, we can eliminate the combinations that have multiple possibilities for the oldest daughter's age:
1 + 72 = 73 - There is a unique oldest daughter (age = 72)
2 + 36 = 38 - Both ages can be shared. This combination is excluded since it doesn't provide a unique oldest daughter.
3 + 24 = 27 - Both ages can be shared. Excluded.
4 + 18 = 22 - Both ages can be shared. Excluded.
6 + 12 = 18 - Both ages can be shared. Excluded.
8 + 9 = 17 - Both ages can be shared. Excluded.
Therefore, the unique possibility is when the three daughters' ages are 8, 9, and 72. The census-taker used the provided clue about the oldest daughter's preference for chocolate milk to deduce her age (72) since it was not shared by any of the other two daughters.