Question

Matt Walker is paid weekly and earns a 3.5% straight commission on sales of $6,500 or less and 5% on sales in excess of $6,500. Last week, Matt’s total graduated commission was $415. What were his total sales for the week?

Answer 1

His sales were $7558.82.

Let x be the amount of sales greater than 6500.  He earns 5% commission on these sales, which we represent as 0.05x.

Since he earns 3.5% on sales less than or equal to 6500, we can represent this as 0.035(x-6500).

Together, his commission was 415:
0.05x+0.035(x-6500) = 415

Using the distributive property, we have
0.05x+0.035*x-0.035*6500 = 415
0.05x + 0.035x - 227.5 = 415

Combining like terms gives us
0.085x - 227.5 = 415

Add 227.5 to both sides:
0.085x - 227.5 + 227.5 = 415 + 227.5
0.085x = 642.5

Divide both sides by 0.085:
0.085x/0.085 = 642.5/0.085
x = 7558.82