Common Core Jewelry Creations

Station #1

You are selling your own jewelry creations at the weekly Swap Meet. In order for you to set up a table at the Swap Meet you must first pay the organizers $60. You price your jewelry at the competitive price of $10 per piece. Let P(x) be the profit you make from selling x pieces of jewelry.

1. What is the y-intercept of P(x) and what does it mean in context?

2. What is the slope of P(x)? Explain why it is positive or negative.

3. What is the slope-intercept form of P(x)?

4. How much jewelry do you need to sell in order to break even?

5. How much profit do you earn if you sell 20 pieces of jewelry?

Your jewelry is doing so well that you decide to increase the price to $20 per piece.

6. Give the new profit formula Q(x) of selling x pieces of jewelry with this new price.

7. How much jewelry do you need to sell in order to break even with this new price?

8. How much profit do you earn with this new price if you sell 20 pieces of jewelry?

Station #2

Common Core Surf Lessons

You want to offer surf lessons and charge $25 for a one-hour lesson. You’d like to set up shop in the parking lot across the street from Kalama Beach Park, but the owner of the lot charges $200 to use his parking lot for the day. Let P(x) be the profits you make from giving x surfing lessons.

1. What is the y-intercept of P(x) and what does it mean in context?

2. What is the slope of P(x)? Explain why it is positive or negative.

3. What is the slope-intercept form of P(x)?

4. How many lessons do you need to give in order to break even?

5. How much profit do you earn if you gave 20 lessons?

Because you are so tired from all of the beginner surf lessons, you decide to increase your surf lesson charge to $75.

6. Give the new profit formula Q(x) of giving x hours of surf lessons with this new price.

7. How many hours of lessons will you need to give in order to break even with this new price?

8. How much profit do you earn with this new price if you give 20 lessons?

Station #3

Common Core Shaved Ice

At the First Friday block party in Wailuku, you have the opportunity to set up a booth and sell your famous shaved ice. However, the block party organizer is asking for a percentage of your sales (10%) instead of charging you a flat fee for the booth. You plan on charging your customers $5 for each flavored ice cone. Let P(x) be the profit made from selling x snow cones.

1. What is the y-intercept of P(x) and what does it mean in context?

2. What is the slope of P(x)? Explain why it is positive or negative.

3. What is the slope-intercept form of P(x)?

4. How many snow comes do you need to sell in order to break even?

5. How much profit do you earn if you sell 20 snow comes?

You decide that it may be more profitable to pay a flat fee for renting a booth (and not pay the organizer any percentage of the snow cone income). So, you negotiate to pay a flat fee of $50.

6. Give the new profit formula Q(x) of selling x snow cones under this new scenario.

7. How many snow cones will you need to give in order to break even under this new scenario?

8. How much profit do you earn now if you sell 20 snow cones?

Station #4

Common Core T-shirts

You want to print your favorite math equation on T-shirts and give them to your friend as gifts. You contact your local silkscreener, and she tells you that there is a $30 set-up fee and that each shirt costs $7 to make. Let P(x) be the price of purchasing x shirts.

1. What is the y-intercept of P(x)? What does it mean in context?

2. What is the slope of P(x)?

3. What is the slope-intercept form of P(x)?

4. How much would it cost to buy 20 shirts?

5. If you have $100 to spend on the T-shirts, how many can you buy?

You want to save some money, so ask the prices at another silkscreener, who charge a $35 set-up fee and then charges $5 per shirt.

6. Give a formula for Q(x), the new cost of buying x shirts from the new silk-screener.

7. With this new silkscreen, how many T-shirts can you buy with $100?

8. How much would it cost to buy 20 shirts from the new silkscreener?