tilissa was on the middle rung of a ladder.she went up 3 rungs,thendown 5 rungs and then up 7 rungs where she rested.later she climbed up the remaining 7 rungs on the ladder.how many rungs did the ladder have?
To have a middle rung, the number of rungs must be odd
e.g. if she is on rung #7, there would be 13 rungs
6 below her, and 6 above her, she is on #7
So assume she is on rung #x
so there are 2x-1 rungs
x+3 - 5 + 7 = 2x-1
-x = -6
x = 6
The ladder had 2(6) -1 or 11 rungs
check:
she started at 6,
went up 3 , was on 9
went down 5, was on 4
went up 7, was on 11, the top rung
(Very dangerous to stand on the top rung of a ladder.)
25
To find the total number of rungs on the ladder, we need to add up Tilissa's movements. Let's break down the problem step by step:
1. Tilissa went up 3 rungs. The ladder now has a total of 3 rungs.
2. Then, she went down 5 rungs. If we subtract these 5 rungs from the current total (3 rungs), we get -2 rungs, which is not possible. So, we can conclude that the ladder must have more than 5 rungs.
3. Next, she went up 7 rungs. So far, Tilissa has gone up a total of 3 + 7 = 10 rungs. The ladder now has a total of 10 rungs.
4. Tilissa rested after climbing 7 rungs. This means she is currently on the 10th rung. From here, she climbs the remaining 7 rungs. This brings the total number of rungs to 10 + 7 = 17 rungs.
Therefore, the ladder must have had 17 rungs in total.