Question

HELP. the staircase at the lighthouse tower has between 80 and 90 steps. if matt goes 2 steps at a time then 1 step is left at the end. If he goes 3 steps at a time then 2 steps are left. If he goes 4 steps at a time then 3 steps are left. How many steps are in the staircase?

Answer 1

90

Explanation:

start from the beginning, then if you go 2 steps at a time, then you have 1 step left over at the end, let's assume the length of the stair case is x, so then we will be going up 2/3x steps, and have 1/3 x steps left.

2/3 x = somewhere between 80 and 90, so that means it must be divisible by 3, so 81,84,87,90

3/5 x ==> only 90