WORD PROBLEMS WITH OPERATIONS Algebra 1. The table shows the annual profits of two piano manufacturers. Which manufacturer had the greater total profit.

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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 YearProfit (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 = – = – ( ) = – = 9.7 Manufacturer B: Total profit = – = – = 9.6 = – ( )

STEP 2: Manufacturer A: 9.7 Manufacturer B: 9.6 Compare the total profits 9.7 > 9.6 So, 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? YearProfit (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 = – – 1.7 = 8 Manufacturer B: Total profit = – – 2.1 = (– 5.8 – 1.7) + ( ) = – = (– 6.5 – 2.1) + ( ) = – = 7.5

STEP 2: Manufacturer A: 8 Manufacturer B: 7.5 Compare the total profits 8 > 7.5 So, 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, 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. = – 84 ANSWER 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 of new 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 – foot per year. Approximate the elevation in 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 STEP 2: Use the elevation in 1900 as the original elevation. The time span 1950 – 1900 = 50 years. New elevation = = (– 6) (– 0.12)(50) = 6410

New elevation = = = (–26.3) Use the elevation in 1950 as the original elevation. The time span 2000 – 1950 = 50 years (– 0.526)(50) STEP 3: Calculate the elevation in The elevation in 2000 was about feet above sea level. ANSWER

Approximate the elevation of Mono Lake in 1925 and in 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 = (– 0.12)(25) = (– 3) = 6413 Calculate the elevation in 1925.

New elevation = = = (–7.89) (– 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 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 = ( 29) + ( 39) + ( 39) + ( 22) 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) = = The mean of the numbers is ANSWER Guided Practice

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