How many dashes are there?

Algebra Level 3

6 6 6 6 number of 6s = 50 = 9 9 9 9 number of 9s = N \large \underbrace{ 6-6-6-\cdots - 6}_{\text{number of 6s }=\, 50} = \underbrace{9-9-9-\cdots - 9}_{\text{ number of 9s }=\, N}

What is N ? N?


The answer is 34.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Naren Bhandari
Feb 5, 2018

6 6 6 6 number of 6’s = 50 = 9 9 9 9 number of 9’s = N 6 6 ( 1 + 1 + 1 + 1 number of 1’s = 49 ) = 9 9 ( 1 + 1 + 1 + + 1 number of 1’s = x ( s a y ) ) \begin{aligned} & \underbrace{ 6-6-6-\cdots - 6}_{\text{number of 6's }=\, 50} = \underbrace{9-9-9-\cdots - 9}_{\text{ number of 9's }=\, N} \\& 6 - 6(\underbrace{1+1+1\cdots + 1}_{\text{number of 1's } =\, 49}) = 9 - 9(\underbrace{1+1+1+\cdots+1}_{\text{number of 1's }=\, x (say)})\end{aligned} From above we get . 6 6.49 = 9 9 x 6.48 = 9 ( 1 x ) x = 33 \begin{aligned} & 6- 6.49 = 9-9x \\ & -6.48 = 9(1-x)\\& \Rightarrow x = 33 \end{aligned} So required numbers of N = 34 N = 34 since N = x + 1 N=x+1 .

Stephen Mellor
Feb 3, 2018

We can evaluate the first 2 terms on either side to equal 0. This means that we are left with 48 × 6 48 \times -6 on the left hand side and ( N 2 ) × 9 (N-2) \times -9 on the right. Therefore, 48 × 6 = 9 ( N 2 ) 48 \times -6 = -9(N-2) 288 = 9 ( N 2 ) -288 = -9(N-2) 32 = N 2 32 = N-2 N = 34 N=\boxed{34}

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...