The functions will be linear equations of the form y=mx+b.
After 16.6 hours
Practice makes perfect
Both clowns offer their services for an initial fixed fee and as well as an hourly rate depending on the number of hours contracted. The cost of both clowns can therefore be described using a linear function of the form
y=mx+b,
where y is the total cost and x is the number of hours. The constant, b, reflects the fixed fee that is independent of the number of hours worked and the slope, m, represents the hourly rate. Using the given information, we can write the following equations:
Clown A:& y=11x+100
Clown B:& y=8x+150
We want to know when the cost, y, of these offers are the same. Let's start by using a table to find this number.
x
11(100
)y
8x(50
y)
13
11( 13)+100
243
8( 13)+150
254
14
11( 14)+100
254
8( 14)+150
262
15
11( 15)+100
265
8( 15)+150
270
16
11( 16)+100
276
8( 16)+150
278
17
11( 17)+100
287
8( 17)+150
286
Using a table, we can only know that the cost of the clowns are equal sometime during the 16th hour of clowning around. To get a more exact answer, we have to equate the two functions
11x+100=8x+150
and solve for x. Solving this equation by using a graphing calculator, we first have to enter the left-hand and right-hand sides of the equation. By pressing the button Y=, we can write the equations on the first two rows.
Having entered the equations, you can plot them by pressing GRAPH.
Woops! To see the point of intersection we need to increase the window setting. We can do that by pressing the button WINDOW on our graphing calculator.
Next, to find the point of intersection, we press CALC (2nd + TRACE) and choose the fifth option in the menu, intersect.
You will see the graph again. Now you have to select the first and second curve, and, finally, guess where the point of intersection is. Make sure you place the cursor as close as possible to the point of intersection.
The solution to the system of equations is
x=16.66 y=283.28
