After simplification, the value of 1-2/1(1+2)-3/(1+2)(1+2+3)-4/(1+2+3) (1+2+3+4)-...-100/(1+2+...+99)(1+2+ ...+100) is a proper fraction in its lowest form. Find the difference of its numerator and denominator.

Acaterer charges $500 plus $30 per guest to cater a wedding. walt and traci don't want to spend more than $8000 on catering. write and solve an inequality in terms of the number of guests, g, that can be invited. a) 30g ? 8000; g ? 267 b) 500g < 8000; g < 16 c) 500 + 30g < 8000; g < 250 d) 500 + 30g ? 8000; g ? 250