Aworm is climbing out of a 20 in. hole. the worm climbs 4 inches during each day and at night falls back 10% of the height the worm is above the hole. at the beginning of the fourth day, how far is the worm from the top of the hole?

First day
ok so 4 inches up means 4 iches above the bottom, 10% of 4 is 0.4, and 4-0.4=3.6

second day
3.6+4=7.6, now 10% of that is 0.76, 7.6-0.76=6.84

third day
6.84+4=10.84, 10% of 10.84 is 1.084, 10.84-1.084=9.756

fourth day, at begining is at the end of third

worm is 9.756 in above the bottom of hole
20-heightup=height from top
20-9.756=10.224

answer is 10.224 inches from top

Ok here we go ..there are plenty of ways to solve such math problems but we will go for the smartest and easiest ..5x+2y=7  -2x+6y=9we rearrange them into the following ..by multiplying the 1st equation by 2 it becomes 10x + 4y = 14we rearrange it and so it becomes 10x = 14 - 4yas for the second equation we multiply it by 5 and rearrange it so it becomes as to the following ..-10x + 30y = 45rearranging so 10x = 30y -45now 10x equals both 14 - 4y and 30y -45so   14 - 4y = 30y -4531 = 26yy= 31/26 = 1.19 or around 1.2so by now we can calculate x easily as  -2x+6y=9so 2x = 6y -9 = 6 * 31/26 - 9 = -1.84  then x = - 0.92 or around -0.9best luck!