word problem

Question

Curt can be paid in one of two ways for the furniture he sells. Plan A: salary of $800 per month plus a commission of 10% of sales. Plan B: Salary of $1200 per month plus a commission of 15% of sales in excess of $8000. For what amount of monthly sales is plan B better than plan A, assuming Curt's sales are always more than $8000?

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 < Plan B

 

let x be the total of Curt's sales, x is the basis of the commission under Plan A, but the first 8000 of sales are excluded, (x - 8000) from the basis of commissions under Plan B.

 

800 + x(0.10) < 1200 + (x - 8000)(0.15)

800 -1200 < (0.15) x - 8000(0.15) - (0.10)x

-400 < (0.15 - 0.10)x - 1200

1200 - 400 < (0.05)x

800 < (0.05)x

800/(0.05) < x

16000 < x