Question

Mike can be paid in one of two ways based on the amount of merchandise he sells:Plan A: A salary of $850.00 per month, plus a commission of 10% of sales, ORPlan B: A salary of $1,050.00 per month, plus a commission of 14% of sales in excess of $7,000.00.For what amount of monthly sales is plan B better than plan A if we can assume that Mike's sales are always more than $7,000.00Write your answer an an inequality involving x, where a represents the total monthly sales.

Answer 1

We are looking for the point at which the compensation from Plan A is less than the compensation from Plan B.

Plan A = 850 +0.1x

Plan B= 1050+(x-7000)(0.14)

Plan A < Plan B

850 +0.1x <1050+(x-7000)(0.14)

then we sill simplify

850+0.1x < 1050+0.14x-980

850+0.1x<70+0.14x

then we isolate the x

0.1x-0.14x<70-850

-0.04x<-780

x>-780/-0.04

x>19500

In this case the monthly sales x need to be greater than 19500 (x>19500), in order that Plan B were better than plan A.