Expert: Scott A Wilson - 10/8/2009

Question
an 8 year old boy named Nathan wants to compare his age with that of his mother and grandfather.  his mother is exactly four times his age and his grandfather is exactly seven times his age. how old is Nathan mother? how old is his grandfather?

a)can you rewrite the problem statement in the form of an equation? if so, what is required for you to rewrite it.

b)can the mothers age be found using the same problem solving strategy as the grandfather's age? please explain.

c)one year from now, will the same relationship exists between Nathan's age and that of his mother and grandfather? please use numbers to illustrate your answer.

d) the relationships between the ages of various family members could have been found without using equations and variables. describe a situation in which it would be necessary to employ the more formal mathematical techniques of variables and equations rather than simple reasoning.

thank you very much

Answer
a) I'll say that the boy is B, the mother is M, and the grandfather is G.
The equations we are given are 4B=M and 7B=G.

b) Yes, it can.  Using the grandfather's age, we know 7B=G, so B=G/7.
We also know that M=4B, so put B=G/7 into that and we get M=4G/7.
So the mom's age is 4/7 of the grandfather.

c) Next year, the equations don't apply.
See, now the boy is 8, the mom is 4B=32, and the grandfather is 7B, which is 56.
Next year, they will be 9, 33, and 57, respectively.
4*9 is not 33 and 7*9 is not 57.

d) One way where you might need equation and when there are several people involed.

Another is when there are several relations to note.  For example,
suppose the age of a boy (B) was was found by taking the age of the mom (M) and saying that
B = 4 + (M²-89)/250.  Given the mom was 33, it might take a few minutes to determine
the boy's age was 8.

Unless, of course, you know that 33²=1089, so 1089-89 is 1000,
and 1000 divided by 250 is 4, and 4+4 is 8.