# LINEAR EQUATIONS

# LINEAR EQUATIONS - SUPPLEMENT

__Do all work on a separate sheet of notebook paper.__

__Do all work on a separate sheet of notebook paper.__

**1. HOUSE APPRECIATION**

A house was purchased for $89,000. Six years later it was appraised at $125,000.

Assume that the value V of the house after its purchase is a linear relationship
of

time t (in years owning the home).

a. Express V in terms of t .

b. How many years after the purchase date was the house worth $103,000?

**2. TEMPERATURE**

The freezing point of water is 0ºC or 32ºF, and the boiling point in 100ºC or
212ºF.

Express Fº in terms of C º. (Express any decimals as fractions .)

**3. NUTRITION**

There are approximately 126 calories in a 2-ounce serving of lean hamburger and

approximately 189 calories in a 3-ounce serving.

a. Write a linear equation for the number of calories in lean hamburger in terms
of

the size of the serving.

b. Use this equation to estimate the number of calories in a 5-ounce serving of
lean

hamburger.

**4. AUTOMOTIVE TECHNOLOGY**

The gas tank of a certain car contains 16 gallons when the driver of the car
begins a trip. Each mile driven by the driver decreases the amount of gas in the
tank by 0.032 gallons.

a. Write a linear equation for the number of gallons of gas in the tank in terms
of

the number of miles driven.

b. Use your equation to find the number of gallons in the tank after driving 150

miles.

c. How far can you drive till you run out of gas?

**5. AIR TEMPERATURE**

The relationship between the air temperature T (in ºF) and the altitude h (in
feet

above sea level) is approximately linear for 0 ≤ h ≤ 20,000. If the temperature
at sea level is 60º, an increase of 5000 feet in altitude lowers the air
temperature about 18º.

a. Write the linear equation that expresses T (y- value ) in terms of h (x-value).

b. Use the above equation to approximate the air temperature at an altitude of

15,000 feet.

c. Approximate the altitude at which the temperature is 0 º. Round to the
nearest

foot.

**6. RECORDS**

In 1930, the record for the 400-meter run was 48.6 seconds. In 1970, it was 43.8

seconds. Let R represent the record in the 400-meter run and t the number of
years

since 1930.

a. Write a linear equation that relates R in terms of t.

b. When did the record become 40.08 seconds?

**7. FLYING LESSONS**

Flying lessons cost $645 for an 8 hour course and $1425 for a 20 hour course.
Both prices include a fixed insurance fee.

a. Express cost, C, in terms of the length of time, t, of the course.

b.

What is the hourly rate of the instruction?

What is the fixed insurance fee?

**8. SALES**

A vendor has learned that, by pricing caramel apples at $1.25, sales reach 133

caramel apples per day. Raising the price to $2.25 will cause the sales to fall
to 81

apples per day. Let y be the number of caramel apples the vendor sells at x
dollars

each. Write a linear equation that models the number of caramel apples sold per
day when the price is x dollars each.

**9. TELECOMMUNICATIONS**

A cellular phone company offers several different options for using a cellular

telephone. One option, for people who plan on using the phone only emergencies,
cost the user $4.95 per month plus $.59 per minute for each minute the phone is
used.

a. Write a linear equation for the monthly cost of the phone in terms of the

number of minutes the phone is used.

b. Use your equation to find the monthly cost of using the cellular phone for 13

minutes in one month.

**10. CELL PHONE RATES**

Suppose you have a cellular phone with a rate plan that cost $20 per month, with
no additional charge for the first 30 minutes of use, and the $.40 for each
minute or

fraction of a minute after the first 30 minutes.

a. Write an equation that gives the monthly cost C to talk for x minutes, if x
is

less than or equal to 30 minutes.

b. Write an equation that gives the monthly cost C to talk for x minutes, if x
is

greater than 30 minutes.

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