A set of n numbers has the sum s. Eachh number of the set is increased by 20 nultipled by 5 and then decreased by 20. what is the sume of the nmber the new set in terms of s and n

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- Feb 27th 2007, 02:57 PMGodfatherSet's Of numbers
A set of n numbers has the sum s. Eachh number of the set is increased by 20 nultipled by 5 and then decreased by 20. what is the sume of the nmber the new set in terms of s and n

- Feb 27th 2007, 03:19 PMSoroban
Hello, Godfather!

I'll baby-step through this one . . .

Quote:

A set of*n*numbers has the sum*S*.

Each number of the set is increased by 20, multipled by 5 and then decreased by 20.

What is the sum of the numbers of the new set in terms of*S*and*n*?

The original set is: .a + b + c + ... + n .= .S

Each number*x*is changed like this: .5(x + 20) - 20 .= .5x + 80

The new sum is: .(5a + 80) + (5b + 80) + 5a + 80) + ... + (5n + 80)

. . = .5(a + b + c + ... + n) + (80 + 80 + 80 + ... + 80)

. . . . . . . . . . . . . . . . . . . . . . \__________________/

. . . . . . . . . . . . . . . . . . . . . . . . . . . .n terms

Therefore, the new sum is: .5S + 80n