An Auto mechanic charges $45 for a house call plus $30 per hour for any work done For one cilent's house call the mechanic charges a total of T dollars
Which equation represents this situation where h is the number of hours of work done
A - T = 30h +45
B - T = 30(h+45)
C - T = 45h+30
D - T =45(h+30)
If you cannot see the obvious choice, use an example
supposed he worked for 2 hours, the cost would be
30(2) + 45
Now which of your choices matches this pattern?
The equation that represents this situation is:
A - T = 30h + 45
To determine the correct equation that represents the situation, we need to break down the information given.
The mechanic charges $45 for a house call, regardless of the number of hours worked. This means that the $45 is a fixed cost and needs to be included in the equation.
Additionally, the mechanic charges an extra $30 per hour for any work done. This means that the additional cost increases as the number of hours worked increases, resulting in a cost that is dependent on the number of hours worked. Thus, this extra cost should be represented by the variable 30h, where h is the number of hours worked.
Now, we can look at the answer options and compare them with this understanding:
A - T = 30h + 45: This option correctly includes the fixed cost of $45 and represents the additional cost based on the number of hours worked. So, A is a possible equation.
B - T = 30(h + 45): This equation incorrectly groups the entire fixed cost of $45 with the variable 30h. It suggests that $45 is counted as an hourly rate instead of a fixed cost. Therefore, B is not the correct equation for this situation.
C - T = 45h + 30: This equation represents the situation of charging $30 per hour for the work done correctly. However, it misses the fixed cost of $45 for the house call. Therefore, C is not the correct equation.
D - T = 45(h + 30): This equation groups the fixed cost of $45 as a part of the variable 45(h+30). It implies that the cost increases by $45 per hour, which is not accurate. Therefore, D is not the correct equation.
Based on the analysis, the correct equation that represents the situation is:
A - T = 30h + 45.