+0

# Math

+1
54
8

A 66-seat bus picks up 1 passenger at the 1st bus stop, 2 passengers at the 2nd stop, 3 passengers at the 3rd bus stop and so on. When will all the seats in the bus be filled?

Apr 6, 2021

#1
+1

$$\boxed{11}$$ stops will be taken

Apr 6, 2021
#3
+485
+2

How did you get 11? See my solution for how I got 12. I think you might have factored the quadratic the wrong way as $(n+12)(n-11)=0$ or something.

RiemannIntegralzzz  Apr 6, 2021
#4
+2

really? i honestly just used the long way and just added until i got 66, 1+2+3+4+5+6+7+8+9+10+11 is 66, i believe. i may have done it wrong, sorry!

Guest Apr 6, 2021
#5
+485
+2

Wait you were right, I just realized that I actually factored the quadratic the wrong way :)) the irony. Thank you for helping out!

RiemannIntegralzzz  Apr 6, 2021
edited by RiemannIntegralzzz  Apr 6, 2021
#6
+1

ohh well we're all human right?  mistakes always happen :) good job though, your explanation is much more logical than mine lol

Guest Apr 6, 2021
#7
+485
+1

Thank you!

RiemannIntegralzzz  Apr 6, 2021
#2
+485
+2

You have the sequence $1+2+3+4+5+...+(n-1)+n$, so the sum of this will be $\frac{n(n+1)}{2}$.

So, you are looking for $\frac{n(n+1)}{2}=66$.

$n(n+1)=132$

$n^2+n-132=0$

$(n+12)(n-11)=0$.

This means that $n=11$ or $n=-12$. $n$ obviously cannot be negative, so the only solution is $n=11$, so at the $\boxed{11^{th}}$ stop.

Apr 6, 2021
edited by RiemannIntegralzzz  Apr 6, 2021
#8
+118666
+2

66  is  the  sum of the first  n positive integers....so  we  have

N ( N + 1)   / 2    = 66

N ( N + 1)  = 132

N^2  + N  - 132   =   0

(N + 12) ( N -11)  = 0

Since N  is positive....N - 11   = 0  .....N  =11

It will be full after  the 11th stop

Apr 6, 2021