Answer:
(a) C: $36 per hour; B: $38 per hour
(b) C: c = 36(h -1) +52; B: c = 38(h -1) +42
(c) C: $196; B: $194
(d) 270 = 38(h -1) +42; h = 7
(e) Brian charges $270 for working 7 hours
Explanation:
Given a table of costs and hours for hiring DJs Celinda and Brian, you want to know their hourly costs, equations for their costs, cost for 5 hours, and hours for a cost of $270.
(a) Hourly cost
The cost of an additional hour can be found by subtracting the cost for 1 hour from the cost for 2 hours:
Celinda: $88 -52 = $36 . . . . . cost increase per hour
Brian: $80 -42 = $38 . . . . . . . cost increase per hour
(b) Equations
We can use the "point-slope form" equation of a line to write the equations for the costs.
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
Rearranging, this is ...
y = m(x -h) +k
Here, the slope is the cost per hour. A suitable point is the first one in the table. The variables 'c' and 'h' are defined for us.
Celinda: c = 36(h -1) +52
Brian: c = 38(h -1) +42
(c) 5 hours
Using h=5 in each of these equations, we have ...
Celinda: c = 36(5 -1) +52 = 196 . . . . cost for 5 hours
Brian: c = 38(5 -1) +42 = 194 . . . . cost for 5 hours
(d) $270 to Brian
Using the equation for Brian's cost, we simply need to set c=270 to have the equation we need:
270 = 38(h -1) +42 . . . . equation to find hours
The solution to that equation is ...
270 -42 = 38(h -1) . . . . . subtract 42
228/38 = h -1 . . . . . . . . . divide by 38
6 +1 = h = 7 . . . . . . . . . . . add 1. This is the solution.
It would cost $270 to hire Brian for 7 hours.
(e) Description
The solution to the equation for c=270 is h=7. Since h represents the number of hours the DJ is working, this solution tells us Brian will charge $270 for working 7 hours.
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Additional comment
The two equations can be simplified by eliminating parentheses and combining like terms:
Celinda: c = 36h +16
Brian: c = 38h +4
Parts (d) and (e) work together. The "solution" h=7 doesn't mean anything except in the context of the question it is answering. The question is "how many hours for a charge of $270." The value h=7 means the answer is Brian charges $270 for 7 hours' work.