need help with this word problem please!

Question

stuck on this on

 

Kate has a summer job and a swim instructor to earn her college tuition. she gets paid $6 per hour for the first 20 hrs and $9 an hour for each hour in the week worked over 20 hours. Kates goal is to earn at least $174 per week, kate will need how many hours of over time a week?

Answer 1

Rebecca - 

The first step is going to be creating a system of equations that represents the word problem. 

 

x=regular hours worked

y=overtime hours

coefficients represent her hourly pay for those hours

 

6x + 9y = 174

 

Seeing as Kate gets paid $6 for her first 20 hours of work, let's plug 20 into our equation.

 

6(20) + 9y = 174

 

Next, let's multiply.

 

120 + 9y = 174

 

We need to subtract the 120 from 174 so we can isolate y (the number of overtime hours), which is what we're trying to figure out. 

 

9y = 174-120

 

Let's subtract.

 

9y = 54

 

Now, we know that she needs to earn at least 54 dollars from overtime work. Seeing as she gets paid 9 dollars per hour of overtime, let's divide.

 

9y/9 = 54/9

y = 6

 

 

This lets us know that Kate will need to work at least 6 hours of overtime to make her goal of earning $174 per week. 

I hope this was helpful, Rebecca!

Amanda