Linear Functions1.1Solving Linear Equations

• Solve Linear Equations• Write Complete Answers to

application problems.• Determine whether a solution is

reasonable.• Solve literal equations.

While you are on spring break in Fort Lauderdale, Florida, the cost, C, in dollars of your taxi ride from the airport to your hotel can be represented by the equation

C = 2.10 + 2.40m when the ride is m miles long.

a) What will an 8-mile taxi ride cost?

b) How many miles can you ride if you budget $35 for the taxi?

An 8-mile Taxi ride costs $21.30.

m ≈13.708. For $35, you can take a taxi ride of up to 13 miles.

1.1: Solve Linear Equations and write complete answers to application problems.

If a business produces and sells x items,

Revenue: R = price * quantityCost: C = fixed cost + variable cost

Profit: P= Revenue - Cost

Break-Even Point:Level of sales where the profit is 0 or Cost = Revenue

Business Application

3

Penny makes and sells Penny Blossoms. The cost of materials for each blossom is $1 and she initially invested $48. She sells each Penny Blossom for $5.

a) Write the cost functions.b) Write the revenue functions. c) Find the break even point. d) Find the profit function.e) What is her profit if she sells 25 Penny Blossoms?f) How many Penny Blossoms must she sell to make a profit of $260?

Business Application Example

4

A local chiropractor has a small office where she cares for patients. She has $8,000 in fixed costs each month that cover her rent, basic salaries, equipment, and utilities. For each patient she sees, she has an average additional cost of about $15. The chiropractor charges her patients or their insurance company $80.00 for a visit.

a. Write an equation for the total monthly cost when v patient visits are done in a month.

b. What is the total monthly cost if the chiropractor has 100 patients visits during a month?

c. Write an equation for the monthly revenue when v patients visit a month.

v = Number of patient visits in a month at this chiropractor’s office.C = Monthly cost, in dollars, for v patient visits at this chiropractor’s office.

C = 15v + 8000

C = 15v + 8000C = 9500 The chiropractor’s office has a total monthly cost of $9500

if they have 100 patient visits during the month.

R = Monthly revenue, in dollars, for this chiropractor’s office.R = 80v

1.1: Solve Linear Equations and write complete answers to application problems.

A local chiropractor has a small office where she cares for patients. She has $8,000 in fixed costs each month that cover her rent, basic salaries, equipment, and utilities. For each patient she sees, she has an average additional cost of about $15. The chiropractor charges her patients or their insurance company $80.00 for a visit.

d. Write an equation for the monthly profit the chiropractor makes if she has v patient visits in a month.

e. What is the monthly profit when 150 patients visit in a month?

f. How many patient visits does this chiropractor need to have in a month for her profit to be $5000.00?

P = Monthly profit, in dollars, for this chiropractor’s officeP = R – CP = 65v – 8000

P = 65v – 8000P = 1750. This chiropractor’s office has a profit of $1750 in a month with 150 patient visits.

200 = v. For this chiropractor’s office to have a monthly profit of $5000, they would need to have 200 patient visits during the month.

1.1: Solve Linear Equations and write complete answers to application problems.

Determine whether a solution is reasonable.

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Determine whether a solution is reasonable.P is the population of Kentucky in thousands of people.a. P = 3.5 b. P = 4200 c. P = -210

R is the revenue in dollars from selling kettle corn at a two-day Rodeo.b. R = 20b. R = -3000 c. R = 4500

T is the temperature in degrees Fahrenheit at the South Pole.c. T = -50 b. T = 75 c. T = 82

S is a cook’s monthly salary in dollars from working at White Castle Hamburgers.a. S = 10.50b. S = 1,600 c. S = 28,000

t ≈ 0.423

1.1: Solving literal equations

• Solve for a