Question

​Ramona's Garage charges the following labor rates. All customers are charged for at least 0.5 hr.

Answer 1

Answer:

a. The linear function is given by,

y = 60x + 30  [y is in $ and x is in hour and x ≥ 0.5]

  = 60 [for x < 0.5]

b. The total cost of the repair job is,  $ 675 .

Step-by-step explanation:

Let, the linear function describing garage charge( y in $) and no. of hours of repair job ( x in hour) be,

y = mx + c    [for x ≥ 0.5]  -----------(1)

where, m is the slope of the line and c is the y intercept.

Now ,

m = $\frac {90 - 60}{1 - 0.5}$

  = 60  ----------------(2)

Now, putting the value of m and the point (x,y) = (0.5, 60) in (1), we get,

$60 = 60 \times 0.5 + c$ $

⇒ c = 30 ----------------- (3)  

Hence, the linear function is given by,

y = 60x + 30  [y is in $ and x is in hour and x ≥ 0.5] ------------(4)

  = 60 [for x < 0.5]

Now, putting

x = 4 hr 15 min

= $4\dfrac {15}{60}$ hour

= 4.25 hour in (4), we get,

$y = 60 \times 4.25 + 30$  [in $]

= $ 285

So, the total cost of the repair job,

= $ (285 + 390)

= $ 675