aaggar7 wrote:Approach 1
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Let J=18 at start of babysitting
C's maximum age at that time=9

Jane's has stopped babysitting at 22,so the max age of C at that time will be 11.
J's current age = 32
After 10 yrs the C's age will be 11+10=22

Answer = 22

Approach 2
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J started baby sitting started at 18 and current age is 32.Diff is (32-18)= 14
Age of C at start = 9,current age = 9 + 14 = 23

Answer = 23

These are not two approaches, these are calculating the maximum age of the child Jane could have baby-sit at two different points in the time, i.e. when she started baby-sitting and stopped it.

Obviously the greater of the two will be the potential correct answer.

A proper mathematical approach to solve this problem will be as follows...
For example, let us assume at some point of time in the past Jane's age was J and the age of the child she was baby-sitting at that time was C.

According to the question, maximum value of C is J/2.

Now, Jane's current age is 32.
Hence, Jane was J years old (32 - J) years ago.
Hence, the child's current age is C + (32 - J) years.

We need to find the maximum possible value of C + (32 - J)
Hence, we need to maximize C and minimize J.
As maximum value of C depends on J, we'll minimize J first.
Minimum possible value of J is 18 --> Maximum possible value of C is 18/2 = 9

Hence, maximum possible value of C + (32 - J) = 9 + (32 - 18) = 9 + 14 = 23