A census taker came back to a house where a man lived with his three children. The census taker asked, "What is your house number?" The man replied, "The product of my children's ages is 72 and the sum of their ages is my house number." "But that's not enough information," the census taker insisted. "All right," answered the farmer, "the oldest loves cherry pie.
What is the farmer's house number?
Is the answer for this problem 14 or 15?
census taker walked up to the man of the house and asks how old are your 3
children the man says i don't know , but the product of their ages is 72 and
the sum of their ages is my house number. the census taker walks out to the front of the house walks back and says ok i still don't know what the ages are. I forget to tell you the man said the oldest one likes chocolate pudding. the census taker then writes down the ages of the children and
leaves. how old are the children?
What combinations of three numbers multiply out to equal 72 and what are their sums?
Products -
Sums -
If the house number matched any of the sums, the census taker would immediately know the three ages. Since he came back and said he didn't have enough information, it meant that the house number he saw must have appeared more than once in the list of sums and he therefore could not know which of the sums was right. The man's response answered his question.
Can you you see why now?
Good luck.
No, the oldest one likes cherry pie, not chocolate pudding.
"What combinations of three numbers multiply out to equal 72 and what are their sums? " --- There's a lot of possibilities, and I'm simply asking for a direct answer.
And one more thing, the problem is asking the house number of the man, not his children's ages!!!!!!!!!!!!!!!!!!!!!!!
You're losing focus. Pay attention to the numbers, not the food!
3 x 4 x 6 = 72
3 + 4 + 6 = 13
What other combinations can you come up with?
??
How do u find the GCF of a #
1--What combinations of three numbers multiply out to equal 72 and what are their sums?
2--Products: 72x1x1, 36x2x1, 24x3x1, 18x4x1, 18x2x2, 12x6x1, 12x3x2, 9x8x1, 9x4x2, 8x3x3, 6x6x2, 6x4x3.
3--Sums:....... 74,........ 39,....... 28,....... 23,........ 22,...... 19,....... 17,..... 18,......15,....... 14,..... 14,..... 13.
4--If the house number of the house matched any of the sums, the census taker would immediately know the three ages.
5--Since he came back and said he didn't have enough information, it meant that the house number he saw must have appeared more than once in the list of sums and he therefore could not know which of the sums was right.
6--The housewifes response answered his question. Can you see why now?
There was still some question after seeing the sums of the ages. The problem derives from there being more than one set of numbers with the same sum, 2-6-6 and 3-3-8. In as much as the set 2-6-6 does not have "an oldest child" and 3-3-8 does, the ages must have been 3, 3, and 8.
To solve this problem, we need to find the house number based on the information given about the children's ages and their product being 72.
Let's list down the possible combinations of ages for the three children that have a product of 72:
1) 1, 2, and 36
2) 1, 3, and 24
3) 1, 4, and 18
4) 1, 6, and 12
5) 2, 3, and 12
6) 2, 4, and 9
7) 3, 4, and 6
Now, let's calculate the sum of these three ages for each combination:
1) 1 + 2 + 36 = 39
2) 1 + 3 + 24 = 28
3) 1 + 4 + 18 = 23
4) 1 + 6 + 12 = 19
5) 2 + 3 + 12 = 17
6) 2 + 4 + 9 = 15
7) 3 + 4 + 6 = 13
From the given information, the farmer claims that the census taker does not have enough information. This means that there must be more than one possible combination, where the sum of the ages is the same.
In this case, we see that there are two combinations with the same sum:
1) Combination 6: 2, 4, and 9
2) Combination 7: 3, 4, and 6
However, the farmer provides additional information that the "oldest" child loves cherry pie. From the two combinations, only combination 6 has an "oldest" child (9 years old). Therefore, the farmer's house number must be the sum of the ages in combination 6, which is 2 + 4 + 9 = 15.
So, the correct answer is 15, not 14.