To determine how many diamond rings Heidi needs to sell to earn \[tex]$605, let's analyze each of the provided equations to find the correct one that represents the relationship between the number of rings sold and the total commission earned.
Heidi earns \$[/tex]55 for every ring she sells. Therefore, let's denote the number of rings she needs to sell as [tex]\( w \)[/tex].
Here are the equations provided:
A. \[tex]$ 605 - \$[/tex] 55 = [tex]\( w \)[/tex]
This equation subtracts \[tex]$55 from \$[/tex]605, which implies that the result should be the number of rings Heidi needs to sell. However, that does not correctly model the relationship because it doesn't account for the multiplicative factor of the number of rings.
B. \[tex]$ 55 \times \( w \) = \$[/tex] 605
This equation multiplies the number of rings [tex]\( w \)[/tex] by the commission per ring, \[tex]$55. It correctly represents the total earnings Heidi aims to achieve (\$[/tex]605). Therefore, this equation is correct because it states that the product of the number of rings and the commission per ring equals the total amount earned.
C. \[tex]$ 55 - \( w \) = \$[/tex] 605 - [tex]\( w \)[/tex]
This equation subtracts [tex]\( w \)[/tex] from both \[tex]$55 and \$[/tex]605, which does not accurately depict the relationship between the number of rings sold and the total earnings. It simplifies improperly and doesn't set up the correct condition to solve for [tex]\( w \)[/tex].
D. \[tex]$ 55 + \( w \) = \$[/tex] 605
This equation sums the commission per ring with the number of rings to get the total earnings. This is not the correct approach as it implies adding the number of rings and the commission per ring directly without accounting for the fact that each ring contributes \[tex]$55 to the total.
Given these explanations, the correct equation that represents the scenario is:
B. \$[/tex] 55 \times [tex]\( w \)[/tex] = \$ 605
