SOLUTION: A set of staircases grows at a certain rate.If the rule to find out how many blocks are needed total to make a staircase with n number of steps is (n) (n)/2+1/2n=y then what is the

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A set of staircases grows at a certain rate.If the rule to find out how many blocks are needed total to make a staircase with n number of steps is (n) (n)/2+1/2n=y then what is the      Log On


   

Question 118864: A set of staircases grows at a certain rate.If the rule to find out how many blocks are needed total to make a staircase with n number of steps is (n) (n)/2+1/2n=y then what is the rule to find out the number of steps in the staircase if y is given?
ex.n(n)/2+1/2n=105 (solve for n)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
if n represents the number of steps and S%28n%29 represents the total number of blocks, then:


S%28n%29=%28n%2F2%29%2B%281%2F2%29n
or

S%28n%29+=+n%28n%2B1%29%2F2.............(solve for n)
given: S%28n%29+=+105
105+=+n%28n%2B1%29%2F2………..multiply by 2

105%2A2+=+2%2An%28n%2B1%29%2F2

210+=+cross%282%29%2An%28n%2B1%29%2Fcross%282%29
210=+n%28n%2B1%29
210=+n%5E2+%2Bn
n%5E2+%2Bn+-210=0

Use quadratic formula to solve for n; we will need only positive solution

n%5B1%2C2%5D=%28-b+%2B-+sqrt+%28b%5E2+-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29

n%5B1%2C2%5D=%28-1+%2B-+sqrt+%281%5E2+-4%2A1%2A%28-210%29+%29%29+%2F+%282%2A1%29

n%5B1%2C2%5D=%28-1+%2B-+sqrt+%281+%2B+840+%29%29+%2F+2

n%5B1%2C2%5D=%28-1+%2B-+sqrt+%28+841+%29%29+%2F+2

n%5B1%2C2%5D=%28-1+%2B-+29%29+%2F+2

n%5B1%5D=%28-1+%2B+29%29+%2F+2

n%5B1%5D=28+%2F+2

n%5B1%5D=+14……………….. the number of steps in the staircase

Check:
105+=+n%28n%2B1%29%2F2………..
105+=+14%2814%2B1%29%2F2………..
105+=+14%2815%29%2F2………..
105+=+cross%282%29%2A7%2815%29%2Fcross%282%29………..
105+=+7%2815%29………..
105+=+105………..