Ali is paid double time if she works more than 37 hours in a week. One week she ears $653.25. If her normal hourly rate is $9.75, how many hours total worked?

Question

How many hours in total did ali work that week? 

Answer 1

37*($9.75)+$19.50x=$653.25 where x is the number of hours over 37 and double time is 2*$9.75=$19.50

$360.75+$19.50x=$653.25

$19.50x=$653.25-$360.75

$19.50x=$292.50

x=$292.50/$19.50

x=15 hours over 37

total number of hours worked is 37+15=52 hours

Answer 2

Hi Jonathan;

Thank you for another great question!

x=quantity worked beyond 37...

($9.75/hour)(37 hours) + (3/2)($9.75/hour)(x hours)=$653.25

Let's cancel hours...

($9.75/hour)(37 hours) + (3/2)($9.75/hour)(x hours)=$653.25

($9.75)(37)+(3/2)($9.75)(x)=$653.25

Now, let's cancel $...

(9.75)(37)+(3/2)(9.75)(x)=653.25

(360.75)+(14.625)(x)=653.25

Let's subtract 360.75 from both sides, as we proceed to isolate x...

-(360.75)+(360.75)+(14.325)(x)=653.25-360.75

(14.325)(x)=292.50

Let's divide both sides by 14.325...

[(14.325)(x)]/(14.325)=(292.50)/(14.325)

x=20.42 hours

 

She worked 37+20.42 hours=57.42

 

Let's check our work...

37(9.75)+(3/2)(9.75)(20.42) ?? 653.25

360.75+298.64  ?? 653.25

659.39 is close enough to 653.25