I need help solving a few problems

Question

1.  A plumber charges $50 for a house call, plus an additional $30 for each hour he works.  In the last month he has spent 85 hours, earning $4450.  How much did he work?

 

2.  A new car has improved gas mileage of 18%.  If  it can travel 32 mpg, what did the old model get in gas mileage?

 

3.  Last year a company earned $1.2 million in profits.  This year, they lost $0.3 million.  What is the percentage change?

 

Answer 1

I think problem number 1 is unclear.  We might need to know how many house calls were made.  The problem doesn't ask that.  Let's say he had 10 house calls.  The house calls would have resulted in a cash inflow of $500 (i.e. $50 x 10).  With that number we may find by subtraction, the amount of money he received for working: 

$4450 - $ 500 = $3950.  Next at $30/hr, by division we may find the number of hours worked:

Each $30 represents one hour of work.  The number of hours worked equals the number of 30s in 3950.  3950/30 =  131.666....  But now we would need to know if he gets paid for a fraction of an hour, like $15 for half an hour, $7.50 for a quarter of an hour, etc.  If not, then we have a different problem.

 

In a problem that is unclear, one might argue that he spent 84 hours working (earning), and the rest of the money was not really earned.  In that case, his hourly rate would be at least $30; it would be $4450/85 or about $52.36 per hour.

 

When problems are not clear, it takes some guess and check (sort of like I did above) to get a good idea where to begin.  Now after all that thinking above, I think I get it.  I think how much he worked means how many house calls did he make.

 

Let c = the number of house calls:

 

50c + 30(85) =    4450

 

       -  2250   = - 2250

__________       ____

50c               =    1900 

 

 

50c               =  1900

----                   ------

50                       50

 

 

   c                =   38

 

 

I would say the answer is that he made 38 house calls.  That's a lot of work.

 

Now to the next problem:

2. A new car has improved gas mileage of 18%. If it can travel 32 mpg, what did the old model get in gas mileage?

i = initial gas mileage in mpg; the 18% is probably based on the old gas mileage:

 

i + 18% of i     =   32

 

1.18 i              =   32

 

 

1.18 i                   32      

-------             = ------

1.18                    1.18

 

 

        i              =  27.1

 

So the old got about 27 miles per gallon.

 

 

3. Last year a company earned $1.2 million in profits. This year, they lost $0.3 million. What is the percentage change?

this year the company probably earned $(1.2 - 0.3) million or $0.9 million.

But maybe they earned $1.2 million, didn't make any more money and lost $0.3 million, so $0.9 million would be the answer.  I doubt it.

 

The percentage change might be:

0.3/1.2 = 25%; so the change would be 25% less based on last years earnings;

 

The percentage change might be:

0.3/0.9 or about 33% based on this years earnings.

 

You may argue 25% or 33% to justify your position.

 

Well, I hope I have helped.   I don't know as I gave any correct answers, but hopefully helped you think about the problem.

 

 

 

 

 

 

 

 

 

 

Answer 2

1. (do you mean how many house calls? If so)

Let x represent the number of houses he worked at 

 

4450 = 50x + 85(30)

Solve for x,

4450 - 2550= 50x

1900=50x

 

 

x= 38

 

He made 38 house calls.