Problem: A set of n numbers has the sum s. Each number of the set is increased by 20, then multiplied by 5, and then decreased by 20. The sum of the numbers in the new set thus obtained is:
Answer Choices:
A. s+20n
B. 5 s+80n
C. s
D. 5s
E. 5s+4n
Solution:
s1=a1+a2+…+an
s2=5a1+80+5a2+80+…+5an+80
=5(a1+a2+…+an)+80n
=5s+80n
or
∑nai=s
∑n[5(ai+20)−20]=
=5∑nai+∑n80=5s+80n