Word Problem Raul owns his own social bowling

Word Problem • Raul owns his own social bowling club called Operation Bowling Thunder which boasts a daily average of 400 customers. To bowl at Raul’s elite bowling center, Raul currently charges a flat rate of $15 person. Recently, business has been slow and Raul is trying to figure out a way to draw in more money. Elaine is in charge of marketing and found in a recent survey that for every dollar Raul lowers the price, 50 more people will come to the bowling alley. How much should Raul charge in order to maximize revenue?

How to Approach Word Problems 1. 2. 3. 4. 5. 6. Eliminate extra information. Extract main question. Simplify key ideas. Quantify key ideas. Find equation for main question. Solve.

Eliminate Extra Information • Raul owns his own social bowling club called Operation Bowling Thunder which boasts a daily average of 400 customers. To bowl at Raul’s elite bowling center, Raul currently charges a flat rate of $15 person. Recently, business has been slow and Raul is trying to figure out a way to draw in more money. Elaine is in charge of marketing and found in a recent survey that for every dollar Raul lowers the price, 50 more people will come to the bowling alley per day. How much should Raul charge in order to maximize revenue?

Extract Main Idea • How much should Raul charge in order to maximize revenue? • Maximize Revenue. • What is Revenue? • Revenue = cost person * number of people

Simplify key ideas. his own social bowlingevery club called • Raul 400 owns people bowl currently day Operation Bowling Thunder which boasts a daily • Raul charges $15 person average of 400 customers. To bowl at Raul’s elite • bowling For every $1 Raul less currently Raul charges, more center, charges 50 a flat rate of people will bowl. $12 person. Recently, business has been slow and Raul is trying to figure out a way to draw in more money. Elaine is in charge of marketing and found in a recent survey that for every dollar Raul lowers the price, 50 more people will come to the bowling alley per day. How much should Raul charge in order to maximize revenue?

Quantify Key Ideas • 400 people bowl currently every day ØX=0, y=400 (change in cost vs. number of people) • Raul charges $15 person Ø$15 * 400 people = $6000 • For every $1 less Raul charges, 50 more people will bowl Ø$14 * 450 = $6300 Ø$13 * 500 = $6500

Find Equation for Main Question • Maximize Revenue • Revenue = Cost per Person * Number of people • Cost per Person Ø(15 – x) • Number of People Ø (400 + 50 * x) • Equation: y = (15 – x) * (400 + 50 * x)

Solve • Graph : y = (15 – x) * (400 + 50 * x) • Where are the zeroes? Øx = 15 and x = -8 ØMax is halfway between two zeroes for a parabola Ø(15 -8)/2 = 3. 5 • Max is when x = 3. 5 or Raul charges $11. 5 • Y = $(15 – 3. 5) * (400 + 50 * 3. 5) = $(11. 5) * (575) = $6612. 5 HAS-CED. A. 2, HSF-IF. B. 4, 5, 7

Further Understanding • • • What sort of answers would make sense? Could x be negative? What is are reasonable x values? What should be the domain of the function? The range? Why? HAS-CED. A. 2

How to Approach Word Problems 1. 2. 3. 4. 5. 6. Eliminate extra information. Extract main question. Simplify key ideas. Quantify key ideas. Find equation for main question. Solve.