Ray and Stella are both given jobs by the same company. Ray is to be paid a basic salary of $3000 each month. He will get a raise of $100 after the first month and every month thereafter he will get a raise of $100 more than the preceding month. Stella will be paid a basic salary of $1500 for every half-month. At the end of the first half-month she will get a raise of $25 and for every half-month thereafter she will get a raise of $25 more than the preceding half-month. At the end of the year Stella will have made $______ more than Ray.

Answer 1

in the nth month, ray gets 3000+100(m-1) = 2900 + 100m
in the nth half-month, stella gets 1500 + 25(n-1) = 1475 + 25n

The year has 12 months and 24 half-months.

during the year,
ray makes 12/2 (2900 + 2900 + 11*100) = $41,400
stella makes 24/2 (1475 + 1475+23*23) = $41,748