speedy cab has an initial charge of 2.50 plus 3.50 for each additional mile, friendly cab has an initial charge of 5.50 plus an additional 2.00 per mile, write and solve an equation to determine how many miles you must go for the costs to be equal

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18