37 and 29 won't work because these numbers are prime numbers, which can't be divided equally. This problem is basically saying which one of these are prime numbers.
50,000 / 2500 = 20....he bought them for 20 bucks a piece. So if he wants to sell them at 15% profit, he would sell them for 20 + 0.15(20) = $ 23 bucks.
A 15% profit of 50,000 dollars is 0.15(50,000) = 7500. Plus the 50 grand spent totals 57500. So they want to make a $ 7500 profit. Selling 2500 lamps at $ 23 per lamp (2500 x 23 = 57500) makes them their profit.
I should just shut up now...answer is $ 23 per lamp
A hexagon is composed of 6 congruent equilateral triangles. Each equilateral triangle has interior angle of 60 degrees. Adding 6 such angles together gets you to 360 degrees. So we've done one full rotation and covered every bit of the plane surrounding a given point. Extend this out and you'll be able to cover the plane. A similar situation happens with rectangles as well (think of a grid, or think of tiles on the wall or floor)
In contrast, a regular pentagon has interior angle 108 degrees. This is not a factor of 360, so there is no way to place regular pentagons to have them line up and not be a gap or overlap. This is why regular pentagons do not tessellate the plane. The same can be aside about decagons and octagons as well.
