ast week he worked 35 hours & earned $436.60 write & solve an equation to find normal hourly rate,r.

Question

I'm not sure how to do this

 

Julio is paid 1.4 times his normal hourly rate for each hour he works over 30 hours in a week. last week he worked 35 hours and earned $436.60 write and solve an equation to find Julius normal hourly rate,r. Explain how you know that your answer is reasonable

Answer 1

It is nice to see a problem with words like “explain” and “know” and “reasonable.”  Often, problems simply seek answers (and lots of students get answers and learn nothing in the process).

One important item to learn is that units are important.  In this problem, we multiply hours by $/hour to get $ (because the hours cancel out).  Also, in this problem there are two hourly rates (and they are related – by a ratio of 1,4).  The problem specifies the variable r and asks you to find its value.

For the first 30 hours, Julio is paid:      (30 hours)*($r / hour)
For the next 5 hours, Julio is paid:        (5 hours)*($1.4r / hour)
These total $436.60, so add them up:
         30r + 5*(1.4r) = 436                [we’ll remember to put units back on later]
         300r + 5(14r) = 4360            [multiply everything by 10 because I have trouble with decimals]
           370r = 4360                      [collect terms]
                 r = $11.78                [put $ back on]

Now, the general equation involves total hours, h, and is solved the same way:

        Pay = 30*$r + (h-30)*$1.4r     (note: h must be >= 30)

Checking (very important):
    Is 30*11.78 + 5*1.4*11.78   =  436      ?
         353.40 +  82.46  = 436   ?
              435.86  =  436   ?     Well, close.

How do we know we are close to the correct answer (that is, is it “reasonable”)?
   I wish more problems would ask students to estimate and to think.  This rationale may vary with the student.  I’d say that if Julio earned $12/hr (fairly close to our answer), then he would earn:
                 30*$12 = $360 for the first 30 hours
      And, since 40% of 12 is 0.48 (a little less than 0.5), Julio earns a little less than 1.5r for 5 hours.
                  5*1.5*$12 =  5*18 = (10/2)*18 = 180/2 = 90      he earns a little less than $90 extra.
    So, $360 + $90 = $450     Julio should earn a little less than $450 for his 35 hours.  And he did!

(full disclosure:  I picked values that I could calculate in my head.)