Problema Solution
The number of students in Woodsville Elementary School in the year 2005 was a square number. The number of students in the year 2006 was also a square number and it was 101 more than thenumber of students in 2005. What was the number of students in the year 2006?
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let
x^2 = the number of students in 2005
y^2 = the number of student in 2006
y^2 = 101 + x^2
y^2 - x^2 = 101
(y - x)(y + x) = 101*1 (101 is prime number)
we have the following case:
y - x = 1
y + x = 101
by solving we find:
x = 50
y = 51
click here to see the step by step solution of the system of equations:
51^2 = 2601 students
there were 2601 students in 2006.