Problema Solution
The room numbers on one side of a school corridor are consecutive positive even integers. The product of the room numbers for two adjoining rooms on that side is 5624. Find the room numbers.
Answer provided by our tutors
Lets denote the room numbers of 2 adjoining rooms with 'a' and 'b' then we have:
a*b=5624
Let a = 2*n then b = 2*n + 2 = 2*(n+1), where n is positive integer. Thus we have
2*n*(2*n+2) = 5624
2*n*2*(n+1) = 5624
4*n(n+1) = 5624
If we divide by 4 on both sides of the equation we get
n(n+1) = 1406
n^2 + n - 1406 = 0 (quadratic equation)
n = [-1 + (1 + 4*1406)^(0.5)]/2
n = [-1 + 75 ] / 2
n = 37
Lets check the result!
a = 2*n = 2*37 = 74
b = 76
74*76 = 5624
The room numbers are 74 and 76.