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 per 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 per 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 per person * number of
people
Simplify key ideas.
his own
social
bowlingevery
club called
•Raul
400owns
people
bowl
currently
day
Operation Bowling Thunder which boasts a daily
• Raul charges $15 per person
average of 400 customers. To bowl at Raul’s elite
•bowling
For every
$1Raul
lesscurrently
Raul charges,
more
center,
charges50
a flat
rate of
$12
people
per person.
will bowl.
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
X=0, y=400 (change in cost vs. number of people)
• Raul charges $15 per person
$15 * 400 people = $6000
• For every $1 less Raul charges, 50 more
people will bowl
$14 * 450 = $6300
$13 * 500 = $6500
Find Equation for Main Question
• Maximize Revenue
• Revenue = Cost per Person * Number of
people
• Cost per Person
(15 – x)
• Number of People
 (400 + 50 * x)
• Equation: y = (15 – x) * (400 + 50 * x)
Solve
• Graph : y = (15 – x) * (400 + 50 * x)
• Where are the zeroes?
x = 15 and x = -8
Max is halfway between two zeroes for a parabola
(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.