College Algebra

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7

Slide 63

E.g. 7—Carnival Tickets

A carnival has two plans for tickets.

Plan A: $5 entrance fee and 25¢ each ride

Plan B: $2 entrance fee and 50¢ each ride

How many rides would you have to take for plan A to be less expensive than plan B?

Slide 64

E.g. 7—Carnival Tickets

We are asked for the number of rides for which plan A is less expensive than plan B.

So, let: x = number of rides

Slide 65

E.g. 7—Carnival Tickets

The information in the problem may be organized as follows.

Slide 66

E.g. 7—Carnival Tickets

Now, we set up the model.

Cost with plan A < Cost with plan B

5 + 0.25x < 2 + 0.50x

3 + 0.25x < 0.50x (Subtract 2)

3 < 0.25x (Subtract 0.25x)

12 < x (Divide by 0.25)

So, if you plan to take more than 12 rides, plan A is less expensive.

Slide 67

E.g. 8—Fahrenheit and Celsius Scales

The instructions on a box of film indicate that the box should be stored at a temperature between 5°C and 30°C.

What range of temperatures does this correspond to on the Fahrenheit scale?

Slide 68

E.g. 8—Fahrenheit and Celsius Scales

The relationship between degrees Celsius (C) and degrees Fahrenheit (F) is given by:

C = 5/9(F – 32)

Expressing the statement on the box in terms of inequalities, we have: 5 < C < 30

Slide 69

E.g. 8—Fahrenheit and Celsius Scales

So, the corresponding Fahrenheit temperatures satisfy the inequalities

Slide 70

E.g. 8—Fahrenheit and Celsius Scales

Thus, the film should be stored at a temperature between 41°F and 86°F.