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?
To find out how many widgets Mr. Smith sold, let's break down the given information:
1. Mr. Jones makes a 3% commission on his sales of widgets.
2. Mr. Smith makes a 5% commission on his sales of widgets.
3. Mr. Smith sold 500 fewer widgets than Mr. Jones.
4. Both Mr. Jones and Mr. Smith earned the same commission.
Let's start by setting up equations based on the given information:
Let's say Mr. Jones sold x number of widgets.
So, Mr. Smith sold x - 500 widgets since he sold 500 fewer widgets than Mr. Jones.
Now, let's calculate the commission earned by both Mr. Jones and Mr. Smith:
Commission earned by Mr. Jones = 0.03 * x
Commission earned by Mr. Smith = 0.05 * (x - 500)
The problem states that both Mr. Jones and Mr. Smith earned the same commission. So, we can set up the equation:
0.03 * x = 0.05 * (x - 500)
Let's solve this equation to find the value of x:
0.03 * x = 0.05 * x - 0.05 * 500
0.03 * x - 0.05 * x = -0.05 * 500
-0.02 * x = -25
Divide both sides of the equation by -0.02:
(-0.02 * x) / (-0.02) = (-25) / (-0.02)
x = 1250
Therefore, Mr. Jones sold 1250 widgets.
Now, we can calculate the number of widgets Mr. Smith sold:
Mr. Smith sold x - 500 = 1250 - 500 = 750 widgets.
So, Mr. Smith sold 750 widgets.