1. WORD PROBLEMS WITH OPERATIONS Algebra 1

2. 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

3. 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)

4. 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.

5. 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….

6. 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

7. STEP 2: Manufacturer A: 8 Manufacturer B: 7.5 Compare the total profits 8 > 7.5 So, manufacturer A had the greater total profit.

8. 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

9. STEP 1: Write a verbal model. Then write an equation. C = m - n

10. 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.

11. 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

12. 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

13. 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

14. 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

15. 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:

16. 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

17. 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

18. 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

19. 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.

20. 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.

21. Mean The average of a set of data Vocabulary

22. 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

23. 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

24. 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 0.375 ANSWER Guided Practice

25. 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

26. 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