Lesson 7.12 Practice Worksheet Lesson 7.12: Practice
Systems of Equations & Break-Even Points
Name:
Date:
Independent Practice
Model each scenario by writing two linear equations. Complete the table of values to find your coordinate pairs, then graph both lines on the coordinate plane. Identify the Break-Even Point (x, y) where both options cost the exact same amount.
Problem 1: Gym Membership
Gym A charges a registration fee of $50 plus a monthly membership fee of $10. Gym B has no registration fee but charges $20 per month. After how many months will the total cost for both gyms be exactly the same?
Gym A Eq:
y = ________
Gym B Eq:
y = ________
Months (x) Gym A ($) Gym B ($) 0 2 5 10
Total Cost ($)
$200$150$100$50$0
0246810
Months
Break-Even Point: (_____, _____)
Problem 2: Bike Rentals
Beach Bikes charges a base fee of $10 plus an hourly rate of $5 for rentals. Cruiser Co. has no base fee but charges a higher rate of $7 per hour. At what point will both rental companies cost the same?
Beach Eq:
y = ________
Cruiser Eq:
y = ________
Hours (x) Beach ($) Cruiser ($) 0 5 10
Total Cost ($)
$100$75$50$25$0
0246810
Hours
Break-Even Point: (_____, _____)
Problem 3: Tutoring Packages
Smart Start charges a one-time consultation fee of $60 plus $10 per hour. Go Genius charges a flat rate of $30 per hour. At how many hours will both cost the exact same?
Smart Eq:
y = ________
Go Eq:
y = ________
Hours (x) Smart ($) Go ($) 0 3 6
Total Cost ($)
$150$100$50$0
0246810
Hours
Break-Even Point: (_____, _____)
Exit Ticket
Model and solve these final two scenarios.
ET #1: Phone Plan A costs $40 plus $2 per gigabyte used. Phone Plan B costs $20 plus $4 per gigabyte used. Find when the cost is identical.
$100$80$60$40$20$0
0246810
Cost GB
Point: (_____, _____)
ET #2: Lawn Mowing Service A charges $20 flat. Service B charges a $5 fee plus $5 per acre. Find when they cost the same.
$30$25$20$15$10$5$0
012345
Cost Acres
Point: (_____, _____)
Lesson 7.12 Homework Worksheet Lesson 7.12: Homework
Mastering break-even points independently.
Name:
Analyze each situation, write your linear equations, and solve through tables and graphing. Provide the final break-even point as an (x, y) coordinate.
Scenario 1: Party Venues
Venue A charges a rental fee of $100 plus $5 per guest. Venue B charges a $50 rental fee plus a higher cost of $10 per guest. At how many guests is the cost identical?
Venue A Eq:
y = ________
Venue B Eq:
y = ________
Guests (x) A ($) B ($) 0 5 10 15
Total Cost ($)
$200$150$100$50$0
05101520
Guests
Break-Even Point: (_____, _____)
Scenario 2: Food Trucks
Truck A charges $15 for a base platter plus $2 per extra taco ordered. Truck B charges a flat rate of $5 per taco with no platter fee. When is the price the same?
Truck A Eq:
y = ________
Truck B Eq:
y = ________
Total Cost ($)
$50$40$30$20$10$0
0246810
Tacos
Break-Even Point: (_____, _____)
Scenario 3: Photo Printing
Store A charges a flat rate of $0.50 per photo printed. Store B charges a shipping fee of $5 plus only $0.25 per photo. When is the total cost identical?
Store A Eq:
y = ________
Store B Eq:
y = ________
Photos (x) A ($) B ($) 0 20 40
Total Cost ($)
$25$20$15$10$5$0
010203040
Photos
Break-Even Point: (_____, _____)
Lesson 7.12 Worksheet Lesson 7.12
Skills Refresh, Guided Challenge, & Mastery Practice
Name:
Do Now: Skills Refresh
Identify the equations, complete the table, and solve for the break-even point.
1. Phone Plan A costs $40 monthly plus $2 per GB used. Phone Plan B costs $20 monthly plus $4 per GB used.
Eq A: y = ________
Eq B: y = ________
Cost ($)
$100$50$0
0510
GB
Break-Even Point: (_____, _____)
2. Mowing Service A is a flat $20 per lawn. Mowing Service B is a $5 travel fee plus $5 per acre mowed.
Eq A: y = ________
Eq B: y = ________
Cost ($)
$30$15$0
024
Acres
Break-Even Point: (_____, _____)
Guided Practice: The Mechanic
Mechanic A charges $200 for parts + $50/hr. Mechanic B charges $50 for parts + $75/hr.
A: y = ________
B: y = ________
Cost ($)
$600$450$300$150$0
02468
Hours
Point: (_____, _____)
Independent Practice Round
Model these business scenarios by writing equations and solving with tables and graphs.
1. Dog Walking: Walkies Inc charges $5 plus $10 per walk. Paws-itive Steps charges a flat $15 per walk.
A: y = ________
B: y = ________
Point: (_____, _____)
Lesson 7.12 Answer Key Answer Key: Lesson 7.12
Systems of Equations Mastery Solutions
Do Now Solutions
1. Phone Plan A vs B
Eq A: \(y = 2x + 40\)
Eq B: \(y = 4x + 20\)
Break-Even Point: (10, 60)
2. Mowing Service A vs B
Eq A: \(y = 20\)
Eq B: \(y = 5x + 5\)
Break-Even Point: (3, 20)
Guided Practice: The Mechanic
Equations:
Eq A: \(y = 50x + 200\)
Eq B: \(y = 75x + 50\)
Table Solutions:
x=0
x=4
x=6
Break-Even Point: (6, 500)
Independent Practice Solutions
1. Dog Walking
Eq A: \(y = 10x + 5\)
Eq B: \(y = 15x\)
Point: (1, 15)
2. Internet Service
Eq A: \(y = 10x + 80\)
Eq B: \(y = 20x\)
Point: (8, 160)
3. Museum Pass
Eq A: \(y = 5x + 50\)
Eq B: \(y = 15x\)
Point: (5, 75)
Exit Ticket Solutions
ET #1: Scooter Rental
Eq A: \(y = 0.50x + 2\)
Eq B: \(y = 0.10x + 6\)
Point: (10, 7)
ET #2: Window Washing
Eq A: \(y = 10x + 30\)
Eq B: \(y = 15x\)
Point: (6, 90)
