EXAMPLE 2 Look for a pattern

Paramotoring

A paramotor is a parachute propelled by a fan-like motor. The table shows the height h of a paramotorist t minutes after beginning a descent. Find the height of the paramotorist after 7 minutes.

EXAMPLE 2 Look for a pattern

SOLUTION

The height decreases by 250 feet per minute.

You can use this pattern to write a verbal model for the height.

An equation for the height is h = 2000 – 250t.

EXAMPLE 2 Look for a pattern

So, the height after 7 minutes is h = 2000 – 250(7) = 250 feet.

ANSWER

EXAMPLE 3 Draw a diagram

BannersYou are hanging four championship banners on a wall in your school’s gym. The banners are 8 feet wide. The wall is 62 feet long. There should be an equal amount of space between the ends of the wall and the banners, and between each pair of banners. How far apart should the banners be placed?

SOLUTION

Begin by drawing and labeling a diagram, as shown below.

EXAMPLE 3 Draw a diagram

From the diagram, you can write and solve an equation to find x.

x + 8 + x + 8 + x + 8 + x + 8 + x = 62

5x + 32 = 62

Subtract 32 from each side.5x = 30

x = 6 Divide each side by 5.

Combine like terms.

Write equation.

The banners should be placed 6 feet apart.

ANSWER

EXAMPLE 4 Standardized Test Practice

SOLUTION

STEP 1 Write a verbal model. Then write an equation.

An equation for the situation is 460 = 30g + 25(16 – g).

EXAMPLE 4 Standardized Test Practice

Solve for g to find the number of gallons used on the highway.

STEP 2

460 = 30g + 25(16 – g)

460 = 30g + 400 – 25g

460 = 5g + 400

60 = 5g

12 = g

Write equation.

Distributive property

Combine like terms.

Subtract 400 from each side.

Divide each side by 5.

The car used 12 gallons on the highway.

ANSWER The correct answer is B.

CHECK: 30 12 + 25(16 – 12) = 360 + 100 = 460

GUIDED PRACTICE for Examples 2, 3 and 4

SOLUTION

2. PARAMOTORING: The table shows the height h of a paramotorist after t minutes. Find the height of the paramotorist after 8 minutes.

The height decreases by 210 feet per minute.

–210 –210 –210 –210

2400 2190 1980 1770 1560

GUIDED PRACTICE for Examples 2, 3 and 4

An equation for the height is h = 2400 – 210t.

h = 2400 – 210 t

So, the height after 8 minutes is h = 2400 – 210(8) = 720 feet.

ANSWER

You can use this pattern to write a verbal model for the height.

GUIDED PRACTICE for Examples 2, 3 and 4

3.

SOLUTION

WHAT IF? In Example 3, how would your answer change if there were only three championship banners?

Begin by drawing and labeling a diagram, as shown below.

From the diagram, you can write and solve an equation to find x.

GUIDED PRACTICE for Examples 2, 3 and 4

x + 8 + x + 8 + x + 8 + x = 62

4x + 24 = 62

Subtract 24 from each side.4x = 38

x = 9.5 Divide each side by 4.

Combine like terms.

Write equation.

The space between the banner and walls and between each pair of banners would increase to 9.5 feet.

ANSWER

GUIDED PRACTICE for Examples 2, 3 and 4

SOLUTION

4. FUEL EFFICIENCY A truck used 28 gallons of gasoline and traveled a total distance of 428 miles. The truck’s fuel efficiency is 16 miles per gallon on the highway and 12 miles per gallon in the city. How many gallons of gasoline were used in the city?

STEP 1 Write a verbal model. Then write an equation.

428 16 g12(28 – g)= +

GUIDED PRACTICE for Examples 2, 3 and 4

Solve for g to find the number of gallons used on the highway.

STEP 2

428 = 16(28 – g) + 12g

428 = 448 – 16g + 12g

428 = 448 – 4g

– 20 = – 4g

5 = g

Write equation.

Distributive property

Combine like terms.

Divide each side by 4.

The car used 5 gallons on the highway.

CHECK: 16(28 – 5) + 12 5 = 368 + 60 = 428

An equation for the situation is 428 = 16(28 – g) + 12g .

Subtract 428 from each side.