Select the correct answer.
Marcus earns a commission of $\frac{1}{10}$ of the price of every electrical appliance he sells. He also spends $10 on lunch each day. If he sells goods worth $x$ dollars in a day, which expression represents the amount of commission he has left after buying lunch? If he sells goods worth $3,500 in one day, how much of his commission does he have left after buying lunch?
A. The expression is $\frac{z+10}{10}$, and the remaining commission is $351.
B. The expression is $\frac{x-10}{10}$, and the remaining commission is $349.
C. The expression is $\frac{x}{10}-10$, and the remaining commission is $340.
D. The expression is $\frac{x}{10}+10$, and the remaining commission is $360.
Answer (1)
Calculate Marcus' commission: 10 x .
Subtract the cost of lunch: 10 x − 10 .
Substitute x = 3500 to find the remaining commission: 10 3500 − 10 .
Simplify to find the remaining commission: $340 .
Explanation
Understanding the Problem Let's break down this problem step by step. Marcus earns a commission based on his sales, but he also has a daily lunch expense. We need to find an expression for his remaining commission after lunch and then calculate this amount for a specific sales value.
Calculating the Commission First, let's determine how to represent Marcus' commission. He earns 10 1 of his sales, which we'll call x . So, his commission is 10 1 x , which can also be written as 10 x .
Subtracting Lunch Cost Next, we need to account for his lunch expense. He spends $10 on lunch each day, so we subtract this from his commission. This gives us the expression 10 x − 10 .
Calculating Remaining Commission Now, let's calculate his remaining commission if he sells $3 , 500 worth of goods. We substitute x = 3500 into our expression: 10 3500 − 10 .
Simplifying the Expression Let's simplify this expression. 10 3500 = 350 , so we have 350 − 10 = 340 . Therefore, his remaining commission is $340 .
Selecting the Correct Answer Comparing our expression and calculated remaining commission with the options provided, we see that option C matches our results.
Examples
Imagine you're a salesperson earning a commission on each sale you make, but you also have daily expenses like transportation or meals. This problem helps you calculate how much of your commission you actually take home after covering those expenses. For instance, if you sell electronics and get 10% commission but spend $10 on travel each day, knowing how to calculate your net earnings helps you manage your finances and set realistic sales goals. This is a practical application of understanding expressions and evaluating them for real-world financial planning.
