Maths
posted by Jane .
"How old are your three children?" the maths teachers ask a former student. He is told their ages add to 13, and multiply to give the number on his study door (which they can both see). "i will need to know more", the master days, after a few moments relfection. "the eldest one is learning to play the violin", replies his former pupil. "ah! in that case i can now give you their ages", the master tells him, and does so correctly. How does he know? what are their ages? what is the number of the door?

1. list all the possible ages of the children (you don't need to, cos i've done it for you) 
eg. (1, 1, 11) (1, 2, 10) etc
2. if you list all this, you will find that there are 2 answers that give a solution of 36. these are:
(6, 6, 1) and
(9, 2, 2)
3. the master says he needs to know more, because there are solutions from which he must choose, and in order to get the right answer, he needs one more clue.
4. the former student says that "his eldest son...", meaning that in the 3 sons, there is one that is older than the rest.
5. from the 2 options listed:
(6, 6, 1) and (9, 9, 2), we can see that (9, 2, 2) is obviously the answer, because the 9 year old is older than the rset, whereas in the other case, there are two sons with the same age of 6.
6. their ages are 9, 2, and 2, and the number on the door is 36. 
The mathematician will only beed to know more if there are two products that are the same (36), 1,6,6, or 2,2,9. In the question it mentions an 'eldest' son, meaning that there is only 1 eldest son (not twins). Therefore their ages are: 2,2,9 and the office number is 36.
Respond to this Question
Similar Questions

Math
In a little town in West Michigan lives a math professor, who hears one day that the barber has three children. So, on the next visit to the barber, the professor casually inquires, "I have heard you have three children, is that right? 
Math Riddle
In a little town in West Michigan lives a math professor, who hears one day that the barber has three children. So, on the next visit to the barber, the professor casually inquires, "I have heard you have three children, is that right? 
math
Ok here is the problem: A hostess said to Mrs. Raines " I have three sons, the product of there ages is 72, the sum of there ages is my house number." ( it desnt give the house number.) Then it says that mrs. Raines needed more info. … 
math
Which of the following is a subset of set A? 
Math
The census taker says, "I need to know the ages of your children." The mother replies, "I have no oneyearolds. The product of my children's ages is 90, and the sum of their ages is the same as my house number." The census taker replies. … 
Math
In a group of 40 students, all students study maths, 28 study biology and math, 20 students study geography and maths and x students study all three subjects. a. Draw a venn diagram to represent the information above, showing in terms … 
Math
There are 21 pupils who study Maths, 29 pupils who study french, 26 pupils who study history. there are 4 pupils who study both maths and french. 10 pupils who study both french and history and 3 pupils who study both maths and history. … 
Maths
I am thinking of a number. I multiply it by 8 and add 15. I get the same answer if I multiply by 2 and add 81. 
maths
mary is now three times as old as susan. Three years ago,the sum of their ages was 22. how old is susan now 
math
Bill ran into his neighbor from across the hall and asked her how old her children were. She replied, “Let’s see if you can figure it out. The product of their ages is 72 and the sum of their ages is the same as my apartment number.” …