Mr. Jones makes 3% commission on his sales of widgets. At a different company,

Mr. Smith makes 5% commission selling the same widgets at the same price. Mr. Smith
sold 500 fewer widgets than Mr. Jones, and they both earned the same commission.
How many widgets did Mr. Smith sell?

.03 j = .05 s

j = s + 500

To find out how many widgets Mr. Smith sold, we can follow these steps:

Step 1: Let's assume Mr. Jones sold x widgets.
Step 2: Mr. Jones earned a 3% commission for selling those x widgets.
Commission earned by Mr. Jones = 0.03 * x
Step 3: Mr. Smith sold 500 fewer widgets than Mr. Jones.
Therefore, Mr. Smith sold (x - 500) widgets.
Step 4: Mr. Smith earned a 5% commission for selling those (x - 500) widgets.
Commission earned by Mr. Smith = 0.05 * (x - 500)
Step 5: According to the given information, the commissions earned by Mr. Jones and Mr. Smith are equal.
0.03 * x = 0.05 * (x - 500)
Step 6: Solve the equation to find the value of x, which represents the number of widgets Mr. Jones sold.
0.03x = 0.05(x - 500)
0.03x = 0.05x - 25
0.02x = 25
x = 25 / 0.02
x = 1250

Therefore, Mr. Jones sold 1250 widgets.

To find out how many widgets Mr. Smith sold, substitute the value of x into the expression we found in step 3:
Mr. Smith sold (1250 - 500) widgets
Mr. Smith sold 750 widgets.

So, Mr. Smith sold 750 widgets.