Sorry for pumping this old one up but I seem to never get it working when J =5 and T =20.
If they have a child every 5 years and their oldest is 20 years then this means that they have
1 child at year 0
2 children at year 5
3 children at year 10
4 children at year 15
5 children at year 20
They have 5 total children right now. After two years, they should have a total of 6.
If I plug in numbers, none of the choices fit.
The answer provided is (A) but if I plug in T + 2 /J + 1 I end up having a non integer.
20 + 2 /5 +1 = 4.5
The numbers you chose are incorrect. If J = 5, T cannot be 20 because they are going to have another child in 2 yrs. Hence T can be 23 or 28 etc but not 20.
If T = 23 and J = 5,
T + 2 /J + 1 = (23 + 2)/5 + 1 = 6 which is correct
Think of it this way:
After 2 yrs, there will be another child. If they have a child every J years, it means (J - 2) yrs have passed since they had their last child.
Let's say T = (J-2) + nJ
n is the number of periods of J years that have passed since T was born. In each one of these periods, one child must have been born.
Re-arranging, n = (T+2)/J - 1
so total number of children the couple will have after 2 yrs is n+2 (+2 to account for T and for the child that will be born 2 yrs from now)
Total number of children = (T+2)/J - 1 + 2 = (T+2)/J + 1
Thank you very much.
Please bear with me for a minute. I am still confused as how landed at 23 or 28. Did you choose these numbers to make sure that they end up being divisible by J? Since we must have an integer as the number of children?