WORD PROBLEMS

WITH OPERATIONS

Algebra 1

The table shows the annual profits of two piano manufacturers.

Which manufacturer had the greater total profit for the three years?

Solve a Multi-Step Problem

Year Profit (millions) for manufacturer

A

Profit (millions) for manufacturer

B

1 – $5.8 – $6.5

2 $8.7 $7.9

3 $6.8 $8.2

STEP 1:Calculate the total profit for each manufacturer.

Manufacturer A:

Total profit

= – 5.8 + 8.7 + 6.8

= – 5.8 + (8.7 + 6.8)

= – 5.8 + 15.5

= 9.7

Manufacturer B:

Total profit

= – 6.5 + 7.9 + 8.2

= – 6.5 + 16.1

= 9.6

= – 6.5 + (7.9 + 8.2)

STEP 2:

Manufacturer A: 9.7 Manufacturer B: 9.6

Compare the total profits

9.7 > 9.6So, manufacturer A had the greater total profit.

Suppose that the profits for year 4 are -$1.7 million for manufacturer A and -$2.1 million for manufacturer B. Which manufacturer has the greater total profit for the four years?

Year Profit (millions) for manufacturer A

Profit (millions) for manufacturer B

1 – $5.8 – $6.5

2 $8.7 $7.9

3 $6.8 $8.2

4 – $1.7 – $2.1

What if….

STEP 1:Calculate the total profit for each manufacturer.

Manufacturer A:

Total profit

= – 5.8 + 8.7 + 6.8 – 1.7

= 8

Manufacturer B:

Total profit

= – 6.5 + 7.9 + 8.2 – 2.1

= (– 5.8 – 1.7) + (8.7 + 6.8 )

= – 7.5 + 15.5

= (– 6.5 – 2.1) + (7.9 + 8.2)

= – 8.6 + 16.1

= 7.5

STEP 2:

Manufacturer A: 8 Manufacturer B: 7.5

Compare the total profits

8 > 7.5So, manufacturer A had the greater total profit.

One of the most extreme temperature changes in United States history occurred in Fairfield, Montana, on December 24, 1924. At noon, the temperature was 63°F. By midnight, the temperature fell to – 21°F. What was the change in temperature?

SOLUTION

The change C in temperature is the difference of the temperature m at midnight and the temperature n at noon.

Evaluate Change

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

C = m - n

STEP 2:Find the change in temperature.

C = m - n

Substitute values.

Write equation.

= – 21 + (-63)Add – 21 and – 63. = – 84ANSWER

The change in temperature was – 84°F.

A new car is valued at $15,000. One year later, the car is valued at $12,300. What is the change in the the value of car?

SOLUTION

The change C in the value of car is the difference of the new car n and the value of the car after 1 year (y).

Guided Practice

Write a verbal model. Then write an equation.

Change in value =Value ofnew car –

Value of car after 1 year

STEP 1:

C = n – y

C = $15000 – $12,300

Write equation.

Find the change in the value of the car after 1 year.

C = $2700

Subtract.

The change in value of the car is $2700.

ANSWER

STEP 2:

C = n – y

In 1900 the elevation of Mono Lake in California was about 6416 feet. From 1900 to 1950, the average rate of change in elevation was about – 0.12 foot per year. From 1950 to 2000, the average rate of change was about – 0.526 foot per year. Approximate the elevation in 2000.

Solve a Multi-Step Problem

New elevation

(feet)

Original elevation

(feet)

Average rate of change (feet/year)

Time passed (years)

= + •

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

Calculate the elevation in 1950.STEP 2:

Use the elevation in 1900 as the original elevation. The time span 1950 – 1900 = 50 years.

New elevation =

= 6416 + (– 6)

6416 +(– 0.12)(50)

= 6410

New elevation =

= 6383.7

= 6410 + (–26.3)

Use the elevation in 1950 as the original elevation. The time span 2000 – 1950 = 50 years.

6410 +(– 0.526)(50)

STEP 3:Calculate the elevation in 2000.

The elevation in 2000 was about 6383.7 feet above sea level.

ANSWER

Approximate the elevation of Mono Lake in 1925 and in 1965.

SOLUTION

STEP 1

Write a verbal model.

New elevation (feet)

Original elevation (feet)

Average rate of change (feet/yr)

Time passed (years)

= + •

Guided Practice

STEP 2

Use the elevation in 1900 as the original elevation. The time span 1925 – 1900 = 25 years.

New elevation = 6416 + (– 0.12)(25)

= 6416 + (– 3)

= 6413

Calculate the elevation in 1925.

New elevation =

= 6402.11

= 6410 + (–7.89)

6410 +(– 0.526)(15)

STEP 3

Use the elevation in 1950 as the original elevation. The time span 1965 – 1950 = 15 years.

Calculate the elevation in 1965.

Mean The average of a set of data

Vocabulary

The table gives the daily minimum temperatures (in degrees Fahrenheit) in Barrow, Alaska, for the first 5 days of February 2004. Find the mean daily minimum temperature.

Find the Mean

Mean

The mean daily minimum temperature was – 30°F.

ANSWER

To find the mean daily minimum temperature, find the sum of the minimum temperatures for the 5 days and then divide the sum by 5.

SOLUTION

=-21 + ( 29) + ( 39) + ( 39) + ( 22) 5

– –––

150 5

–=

= – 30

Find the Mean

Find the mean of the numbers –3, 4, 2, and – 1.5 .

To find the mean, find the sum of the numbers and then divide the sum by 4.

SOLUTION

=– 3 + ( 4) + (2) + (– 1.5) 4 1.5 4=

= 0.375

The mean of the numbers is 0.375ANSWER

Guided Practice

Find the mean daily minimum temperature (in degrees Fahrenheit) in Barrow, Alaska, for the first 5 days of February 2004.

Day in February 1 2 3 4 5

Minimum temperature (°F)

– 3 – 20 – 21 – 22 – 18

Guided Practice

To find the mean daily temperature, find the sum of the minimum temperatures for the 5 days and then divide by 5.

SOLUTION

84 5

–=

= – 16.8

– 3 + (– 20) + (– 21) + (– 22) + (– 18) 5

Mean =

Guided Practice

The mean daily minimum temperature was – 16.8°F.ANSWER