Select the best answer for the question.
Heidi, a jewelry salesperson, earns a commission of $55 every time she sells a diamond ring. How many rings does she have to sell to earn $605? Choose the equation that correctly calculates the amount.
A. $55-w=$605-w
B. $55=w=$605
C. $55+w=$605
D. $605-$55=w
Answer (1)
The problem states Heidi earns $55 per ring and wants to earn $605 in total.
The correct equation should be 55 w = 605 , where w is the number of rings.
Solving for w , we get w = 55 605 = 11 .
None of the options are correct, but option D isolates w , although with incorrect arithmetic. The closest, but still incorrect, option is D .
Explanation
Problem Analysis Let's analyze the problem. Heidi earns $55 for each diamond ring she sells, and she wants to earn a total of $605 . We need to find the equation that correctly represents this situation, where w represents the number of rings she needs to sell.
Setting up the Equation The total amount Heidi earns can be represented as the commission per ring multiplied by the number of rings, which should equal the total earnings she wants to achieve. This can be written as: 55 × w = 605 Now, let's examine the given options to see which one correctly calculates the number of rings.
Analyzing the Options Option A: $55 − w = $605 − w . If we add w to both sides, we get $55 = $605 , which is not true. So, this option is incorrect.
Option B: $55 = w = $605 . This implies that $55 = $605 , which is also incorrect. So, this option is incorrect.
Option C: $55 + w = $605 . This equation suggests that Heidi earns $55 plus some unknown amount w to reach $605 . This is not the correct relationship, as she earns $55 for each ring she sells, not a one-time $55 plus an unknown amount. If we solve for w , we get w = 605 − 55 = 550 . This would mean she needs to sell 550 rings, which doesn't align with the problem statement.
Option D: $605 − $55 = w . This equation calculates w as the difference between the total earnings and the commission per ring. While it gives a numerical value for w , it doesn't represent the original relationship 55 w = 605 . If we calculate w , we get w = 605 − 55 = 550 , which is incorrect.
Solving for w and Re-evaluating Although none of the options directly represent the equation 55 w = 605 , we need to determine which option correctly calculates the number of rings. From the equation 55 w = 605 , we can solve for w by dividing both sides by 55: w = 55 605 .
Calculating the value of w :
w = 55 605 = 11
Now let's re-evaluate the options based on this understanding. Option A: $55 − w = $605 − w is incorrect. Option B: $55 = w = $605 is incorrect. Option C: $55 + w = $605 leads to w = 550 , which is incorrect. Option D: $605 − $55 = w leads to w = 550 , which is also incorrect.
Final Decision However, the question asks for the equation that correctly calculates the amount . Option D, even though it doesn't represent the initial equation, calculates a value for w . However, it's not the correct calculation. Option C is also incorrect. There seems to be an error in the options provided. The correct equation to solve for w should imply w = 55 605 = 11 . However, if we are to choose the best answer among the options, we should look for the one that isolates w on one side. Option D does this, but the calculation is wrong. Option C can be rearranged to w = 605 − 55 , which is also a wrong calculation. Since 605 − 55 = 550 and 55 605 = 11 , none of the options are correct. However, if the question is interpreted as which equation isolates w, then option D is the closest. But the calculation is still wrong.
Conclusion Since none of the options provide the correct equation to directly solve for the number of rings, and there is likely a typo in the question, we should choose the option that at least isolates w on one side, even if the calculation is incorrect. Option D, $605 − $55 = w , isolates w , but the arithmetic is incorrect for the problem. However, it's the closest to isolating w . The correct calculation should be w = 55 605 = 11 .
Examples
Understanding how to calculate earnings based on commission is crucial in many real-world scenarios. For instance, if you're selling products or services, knowing how much you earn per sale helps you set financial goals. If a car salesperson earns a commission of $200 per car and wants to make $5000 a month, they need to sell 200 5000 = 25 cars. This kind of calculation is also useful in understanding sales targets and planning your work to achieve your desired income.
