Fewpal
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in Mathematics by (127k points)

The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.
[Hint : Sx – 1 = S49 – Sx]

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1 Answer

+1 vote
by (39 points)
let x be the value such that the sum of the numbers of the houses preceding the house number x is equal to the sum of numbers following it

⇒sum of  preceding x=sum of following x

1+2+3.....+(x-1)=(x+1)+(x+2).....+49

⇒(x-1)/2*(1+x-1)=(49-x)/2*(x+1+49)

(x-1)/x=(49-x)(x+50)

x^2-x=49x+2540-x^2-50x

x^2-x=2540-x^2-x

2x^2=2540

x^2=1125

x=35

therefore value of x=35

please upvote it

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