#10 step by step

Question

Shaggy earned $8.25 per hour plus an additional $75 in tips waiting tables on Saturday. He earned at least $200 in all. Write an inequality and find the minimum number of hours, to the nearest hour, that Shaggy worked on Saturday

Answer 1

Let X = number of hours that Shaggy worked  

Let Y = Shaggy's earning in dollars

 

Shaggy earned $75 in tips plus $8.25 per hour.  This means that he earned $8.25 times the number of hours that he worked, plus $75.  You can write this as an equation 

 

Y = 8.25*X + 75  

 

We don't know exactly how much Shaggy earned but we know it was at least $200.  So  

 

Y ≥ 200

8.25*X + 75 ≥ 200     (since Y = 8.25*X + 75)  

8.25*X ≥ 125             (subtracted 75 from both sides)  

X ≥ 15.15                   (divided both sides by 8.25)  

 

To make sure Shaggy's earning are at least $200 you have to round up to X = 16 hours  

 

Check:  8.25*16 + 75 = 132 + 75 = $207 which is at least $200

            8.25*15 + 75 = 123.75 + 75 = $198.75 which is not at least $200