let the number be y
17 + (6×y)= 113
17 + 6y = 113
6y = 113-17
your answer is c. 42%
the wording leaves a little to be desired. what does that 32 actually mean?
i don't think it is asking us to add on the distance it has to travel to get a bounce of 32. we are starting with a bounce that is 32 high.
the second bounce is 9/10 of that height which turns out to be 28.8.
the third bounce is 9/10 of 28.8 which is 25.92, i think, and then it continues on.
so here are the givens
a = 32
r = 9/10
n = 25
sum = a(1 - r^n) / (1 - r)
sum = 32*(1 - (9/10)^25) / (1 - 9/10)
sum = 32*(1 - 0.07179) / ( 1 - 9/10)
sum = 32*(0.9282) / 0.1
sum = 29.7 / 0.1
sum = 297
but that number represents only the distance going up. you must also take the distance going down. you have to double this answer.
2*sum = 2 * 297
sum' = 594
the wording is a real snake. we don't really know if we need to include some height that was a start. if we do, the answer is 594 + k where k is a constant yet to be determined. usually k is part of the problem.
or do we take a = 32 as the first drop? we can't tell from the wording.