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?

number for Mr Jones ---- x

number for Mr Smith ---- x-500

.03x = .05(x-500
.03x = .05x - 25
-.02x = -25
x = 1250

Mr. Jones sold 1250 widgets and Mr. Smith sold 750

check:
.03(1250) = 37.5
.05(750) = 37.5

Let's assume that Mr. Jones sold X widgets.

Since Mr. Smith sold 500 fewer widgets than Mr. Jones, Mr. Smith sold (X-500) widgets.

The commission earned by Mr. Jones is 3% of X widgets, which can be expressed as 0.03X.
The commission earned by Mr. Smith is 5% of (X-500) widgets, which can be expressed as 0.05(X-500).

Given that they both earned the same commission, we can set up the following equation:

0.03X = 0.05(X-500)

Simplifying the equation:

0.03X = 0.05X - 25

Combine like terms:

0.05X - 0.03X = 25

0.02X = 25

Divide both sides by 0.02:

X = 1250

Therefore, Mr. Smith sold (1250 - 500) = 750 widgets.

To solve this problem, let's break down the information given and find a solution step by step.

1. We know that Mr. Jones makes a 3% commission on his sales, and Mr. Smith makes a 5% commission on his sales.
2. Let's assume that the price of each widget is the same for both Mr. Jones and Mr. Smith.
3. We need to find the number of widgets that Mr. Smith sold.

Now, let's devise a plan to solve the problem:

Step 1: Set up equations for Mr. Jones and Mr. Smith's commissions.

Let:
x = the number of widgets Mr. Smith sold
x + 500 = the number of widgets Mr. Jones sold

Mr. Jones' commission = 3% of (x + 500)
Mr. Smith's commission = 5% of x

According to the problem, both Mr. Jones and Mr. Smith earned the same commission, so we can set up an equation:

0.03(x + 500) = 0.05x

Step 2: Solve the equation for x.

0.03x + 15 = 0.05x [distributed 0.03 into (x + 500)]
0.05x - 0.03x = 15 [subtracted 0.03x from both sides]
0.02x = 15 [combined like terms]
x = 15 / 0.02 [divided both sides by 0.02]

Using a calculator, we can find that x = 750.

Therefore, Mr. Smith sold 750 widgets.