A radio station advertises a contest with ten cash prizes totaling $5510. There is to be a $100 difference between each successive prize. Find the amounts of the least and greatest prizes the radio station will award.

The ten prizes form an arithmetic sequence with a $100 difference between successive prizes, so the greatest prize is 9 × $100 = $900 more than the least. The average of the first and last prizes is $5510 ÷ 10 = $551, so together they total $1102. Solving for the two amounts gives a least prize of $101 and a greatest prize of $1001, matching choice c.

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