Answer:
235
Step-by-step explanation:
Figure the rates per hr.
110/3 = 36 2/3
160/5 = 32.
So, the rates are not the same.
Knowing a bit about plumbers, they normally charge a basic fee to just show up, and then they charge per hr.
In cases like these, where we're asked to project to a new data point (in this case an 8-hr job), you should immediately think of a graph. The x-axis would be the hours worked. The y-axis would be the charge for the work (the cost of the job).
We're given two pairs of values:
(3,110) and (5,160).
The next step is to fit a line to them.
y = mx+b is the general equation for a line.
m = the slope = rise/run = change in y / change in x
Call the change in y, dy (for delta y).
Call the change in x, dx (for delta x).
m = dy/dx = 50/2 = 25
The slope is thus 25, which means for each hour, the price goes up by $25. That means the plumber charges $25/hr.
We also know the plumber charges $110 for a 3-hr job. 3*25 = $75. So the base charge would be $110-75 = $35.
y = 25x + 35
Checking this formula at x=3, we know it is 110.
Checking it at x=5, we obtain:
y = 25*5 + 35 = 125 + 35 = 160.
That checks.
Now to figure an 8-hr job, set x=8 and use the equation"
y = 25*8 + 35.
y = 200 + 35.
y = 235.
That means an 8-hr job costs $235.
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