Mary's yard is a mess. She needs to hire someone to prune her trees and shrubs. A landscaping service she calls quotes her a price of $[tex]$15$[/tex] consultation fee plus $[tex]$8$[/tex] an hour for the actual work. Mary's neighbor has offered to help her out. She doesn't charge a consultation fee, but does charge $[tex]$10$[/tex] an hour for her work.
Write two equations, one that describes the landscaping service charge and one that describes your neighbor's charge. Let [tex]$C$[/tex] equal the charge as a function of [tex]$h$[/tex], the number of hours worked.
A. [tex]$C=15+10 h$[/tex]
[tex]$C=8 h$[/tex]
B. [tex]$C=10 h+8 h$[/tex]
[tex]$C=15$[/tex]
C. [tex]$C=15+8 h$[/tex]
[tex]$C=10 h$[/tex]
D. [tex]$C=18 h$[/tex]
[tex]$C=15$[/tex]
Answer (2)
Define the charge for the landscaping service as C = 15 + 8 h .
Define the charge for the neighbor as C = 10 h .
The two equations are C = 15 + 8 h and C = 10 h .
The correct answer is c. C = 15 + 8 h , C = 10 h
Explanation
Problem Analysis Let's analyze the problem. We need to write two equations. The first equation should represent the charge of the landscaping service, which includes a consultation fee of $15 and an hourly rate of $8. The second equation should represent the neighbor's charge, which has no consultation fee but charges $10 per hour.
Define Variables Let C 1 be the charge for the landscaping service and C 2 be the charge for the neighbor. Let h be the number of hours worked.
Landscaping Service Equation The landscaping service charges a $15 consultation fee plus $8 per hour. So, the equation for the landscaping service is: C 1 = 15 + 8 h
Neighbor's Equation The neighbor charges $10 per hour and no consultation fee. So, the equation for the neighbor is: C 2 = 10 h
Final Equations Therefore, the two equations are: C = 15 + 8 h C = 10 h This corresponds to option c.
Examples
Imagine you're planning a birthday party and need to rent a venue. One venue charges a flat fee of $50 plus $10 per hour, while another charges $15 per hour with no flat fee. By writing equations for each venue's cost, you can determine which is more cost-effective based on the number of hours you need the venue. This is a practical application of creating and comparing linear equations to make informed decisions about costs.
The equations representing the charges are: C = 15 + 8 h for the landscaping service and C = 10 h for the neighbor. The correct choice from the multiple-choice options is C. These equations capture the cost structure for each helper based on the hours worked.
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