Ms. Zambrano told a census-taker during the recent census that she had three boys. When asked their ages, she replied, “The product of their ages is 72. The sum of their ages is the same as my house number. 1�7
The census-taker looked at the house number and complained, “I still can’t tell! 1�7
Ms. Zambrano replied, “Oh, that’s right. I forgot to tell you that the oldest one likes to play guitar. 1�7
The census-taker promptly wrote down the ages
of the three children.
How old are they? (Due February 1st, 2008)
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4 comments:
Three answers were submitted by Dwayne, Allan, and Vivian, however, no one provided a logical explanation, so please try again. You must explain your solution clearly.
All the possible ages for the three children are:
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 1 36 39
2 2 18 22
2 3 12 17
2 4 9 15
2 6 6 14
3 1 24 28
3 2 12 17
3 3 8 14
3 4 6 13
4 1 18 23
4 2 9 15
4 3 6 13
6 1 12 19
6 2 6 14
6 3 4 13
8 1 9 18
8 3 3 14
9 2 4 15
The numbers that are in the right column are the ages added together. When ma. zambrano told the cencus taker the oldest one likes to play the guitar, that means that there has to be an eldest one. the only ones are when the ages are 6,6, 2 and 8,3,3 because the other ones all add up to a number but all have a eldest one. 6,6,2 doesn't have a eldest one. 6+6+2=14. 8+3+3=14. they both equal 14. 6,6,2 doesn't have a eldest one because there are two 6's. 8,3,3 has a eldest one so it is the age of the three children.
-Vivian Chen
From the list, you could cross out many of them up to the list below:
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
Many of them are able to be crossed out because they are the same combination but in a different order. When you look at this new list, you see that only two of the sums are the same. 2,6,6 and 3,3,8. That was the number the census-taker saw on the house next door even though any of the sums could be the house #. When Ms. Zambrano told the census-taker that the oldest one likes to play guitar, it means that there has to be an eldest child. In 2,6,6 there is no eldest one because there are two children that is 6 years old. In 3,8,8 it is possible because it follows what Ms. Zambrano's clues for her son's ages. Ms. Zambrano's sons ages are 3, 3, and 8.
-Vivian Chen
Hi Ms. Hsiao,
I think the ages of the three children are 3, 4, and 6 respectively. This is because the product of 3x4x6 is 72. Therefore the house number must be 13. I believe these are their ages because the oldest one, 6, likes to play the guitar, which has 6 strings. :) Jonathan Franco
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