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A consulting firm charges r dollars per hour of service plus a flat booking fee of f dollars for each appointment. If a client books two appointments lasting a hours and b hours respectively, what is the total amount charged, in dollars?

Explanation	Calculations	Help
$We translate "r dollars per hour of service" using the rate formula to find the service cost of the first appointment of a hours.$	$Service cost of first appointment = r \times a$	Theory & Tactics Method Card TRANS3-D Click to view full details
$We translate "plus a flat booking fee of f dollars for each appointment" to include the booking fee in the first appointment cost.$	$Cost of first appointment = r \times a + f$	Theory & Tactics Method Card TRANS1-C Click to view full details
$By the same process, we include both the service charge and booking fee for the second appointment of b hours.$	$Cost of second appointment = r \times b + f$	Theory & Tactics Method Card TRANS3-D Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We sum the two appointment costs to get the total amount charged.$	$Total amount = (r \times a + f) + (r \times b + f)$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We combine like terms by adding the r -terms and the f -terms.$	$r (a + b) + 2 f$	Theory & Tactics Method Card CALC1-A Click to view full details

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D

A consulting firm charges r dollars per hour of service plus a flat booking fee of f dollars for each appointment. If a client books two appointments lasting a hours and b hours respectively, what is the total amount charged, in dollars?

Explanation	Calculations	Help
$We translate "r dollars per hour of service" using the rate formula to find the service cost of the first appointment of a hours.$	$Service cost of first appointment = r \times a$	Theory & Tactics Method Card TRANS3-D Click to view full details
$We translate "plus a flat booking fee of f dollars for each appointment" to include the booking fee in the first appointment cost.$	$Cost of first appointment = r \times a + f$	Theory & Tactics Method Card TRANS1-C Click to view full details
$By the same process, we include both the service charge and booking fee for the second appointment of b hours.$	$Cost of second appointment = r \times b + f$	Theory & Tactics Method Card TRANS3-D Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We sum the two appointment costs to get the total amount charged.$	$Total amount = (r \times a + f) + (r \times b + f)$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We combine like terms by adding the r -terms and the f -terms.$	$r (a + b) + 2 f$	Theory & Tactics Method Card CALC1-A Click to view full details

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D