Question

9.

Jacks Plumbing charges customers $100 per hour for repair jobs. Al's Plumbing charges according to the equation y = 75x + 50, where x = time in hours and y = cost

dollars

Explain why Ars Plumbing charges less than Jacks Plumbing for a 4-hour repair job.

Does Als Plumbing charge less than Jacks Plumbing for all repair jobs? Explain why or why not.

Answer 1

As given,

Per hour cost of Jack's plumbing = $100

Also,

Al's plumbing charges = 75x + 50 where x = time in hours .

Now,

Al's plumbing cost for 4 hours:

Here , x = 4

⇒75x + 5 = 75(4) + 50 = 300 + 50 = 350

∴ we get

Al's plumbing cost for 4 hours = $350

Now,

As Jack cost for 1 hour = $ 100

⇒ For 4 hour = 4×$100 = $400

∴ we get

Jack's plumbing cost for 4 hours = $400

As we can see that

$ 400 > $350

⇒Jack's plumbing cost for 4 hours > Al's plumbing cost for 4 hours

Now,

Al's plumbing charges = 75x + 50 where x = time in hours .

For 1 hour

75x + 50 = 75(1) + 50 = 125

Al's 1 hour cost = $125

whereas Jack Plumbing cost for 1 hour = $100

∴ we get

$125 > $100

⇒Al's 1 hour cost > Jack's 1 hour cost

Now,

Al's 2 hour cost

75x + 50 = 75(2) + 50 = 150 + 50 = 200

Al's 1 hour cost = $200

whereas Jack Plumbing cost for 2 hour = $200

∴ we get

$200 = $100

⇒Al's 2 hour cost = Jack's 2 hour cost

Now,

Al's 3 hour cost

75x + 50 = 75(3) + 50 = 225 + 50 = 275

Al's 1 hour cost = $275

whereas Jack Plumbing cost for 3 hour = $300

∴ we get

$275 < $300

⇒Al's 3 hour cost < Jack's 3 hour cost

Als0,

Jack's plumbing cost for 4 hours > Al's plumbing cost for 4 hours

∴ we get

We can not say that Als Plumbing charge less than Jacks Plumbing for all repair jobs.

Because the charge is fluctuating ,

For 1 hour , Aly' charge is grater whereas The 2 hour cost of Jack's is higher.

So, the Correct answer is - No, Al's Plumbing charge is not always less than Jacks Plumbing for all repair jobs.