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# Algebra

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Laverne starts counting out loud by 5's. She starts with 1. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 40, Shirley runs screaming from the room. What number does Laverne say that sends Shirley screaming and running?

May 2, 2024

#1
+202
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Honestly, it's not too hard to just list the numbers and sums out, since the sum we're trying to get is quite small.

 Number Called Out 1 6 11 16 21 26 31 Sum Reached 1 7 17 27 37 47 57

So, when Laverne yells out 31, Shirley would scream out yelling!

:) :) :)

Thanks!

May 2, 2024
#2
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The nth term  = 1 + 5(n  -1)

The sum of the series =  [ first term + last term ] *  number of terms /  2

We can solve this

[  1  +  1 + 5(n - 1) ] (n / 2)  >   40

[ -3 + 5n ] (n)  >  80

5n^2 - 3n - 80  >  0        set   =   0

5n^2  -3n - 80  = 0

We need n to be  an  integer

Use the Quad Formula to find n and  take its ceiling

n  =  ceiling  (  [ 3 + sqrt [ 3^2  - 4 * 5 * -80 ] ] / 10 )   =   5

The number that is  called is    1 + 5(n -1)  = 1 + 5 (5 - 1)  =  1 + 5 (4)   =  21

May 2, 2024
edited by CPhill  May 2, 2024