Algebra 1 Word Problems with Operations
Solve a Multi-Step Problem The table shows the annual profits of two piano manufacturers. Which manufacturer had the greater total profit for the three years?
STEP1: Calculate the total profit for each manufacturer. Manufacturer A: Manufacturer B: Total profit Total profit = – 5.8 + 8.7 + 6.8 = – 6.5 + 7.9 + 8.2 = – 6.5 + (7.9 + 8.2) = – 5.8 + (8.7 + 6.8) = – 6.5 + 16.1 = – 5.8 + 15.5 = 9.6 = 9.7
STEP2: Compare the total profits • 9.7 > 9.6 • So, manufacturer A had the greater total profit. Manufacturer A: 9.7 Manufacturer B: 9.6
What if…. 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?
STEP1: Calculate the total profit for each manufacturer. Manufacturer A: Manufacturer B: Total profit Total profit = – 5.8 + 8.7 + 6.8 – 1.7 = – 6.5 + 7.9 + 8.2 – 2.1 = (– 5.8 – 1.7) + (8.7 + 6.8 ) = (– 6.5 – 2.1) + (7.9 + 8.2) = – 7.5 + 15.5 = – 8.6 + 16.1 = 8 =7.5
STEP2: Compare the total profits • 8> 7.5 • So, manufacturer A had the greater total profit. Manufacturer A: 8 Manufacturer B: 7.5
Evaluate Change 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 mat midnight and the temperature nat noon.
STEP1: Write a verbal model. Then write an equation. C = m - n
STEP2: Find the change in temperature. C = m - n Write equation. = – 21 + (-63) Substitute values. = – 84 Add – 21 and – 63. ANSWER The change in temperature was – 84°F.
Guided Practice 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).
Value of new car Value of car after 1 year – Change in value = STEP1: Write a verbal model. Then write an equation. C = n – y
ANSWER The change in value of the car is $2700. STEP2: Find the change in the value of the car after 1 year. C = n – y Write equation. Subtract. C = $15000 – $12,300 C = $2700
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
+ • Time passed (years) = New elevation (feet) Average rate of change (feet/year) Original elevation (feet) STEP1: Write a verbal model. Then write an equation.
STEP2: Calculate the elevation in 1950. Use the elevation in 1900 as the original elevation. The time span 1950 – 1900 = 50 years. New elevation = 6416 +(– 0.12)(50) = 6416 + (– 6) = 6410
STEP3: Calculate the elevation in 2000. Use the elevation in 1950 as the original elevation. The time span 2000 – 1950 = 50 years. 6410 +(– 0.526)(50) New elevation = = 6410 + (–26.3) =6383.7 ANSWER The elevation in 2000 was about 6383.7 feet above sea level.
Average rate of change (feet/yr) + • New elevation (feet) = Original elevation (feet) Time passed (years) Guided Practice Approximate the elevation of Mono Lake in 1925 and in 1965. SOLUTION STEP 1 Write a verbal model.
STEP 2 Calculate the elevation in 1925. 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
STEP 3 • Calculate the elevation in 1965. Use the elevation in 1950 as the original elevation. The time span 1965 – 1950 = 15 years. New elevation = 6410 +(– 0.526)(15) = 6410 + (–7.89) =6402.11
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
– – – – -21 + ( 29) + ( 39) + ( 39) + ( 22) = 5 150 – = 5 – 30 = The mean daily minimum temperature was – 30°F. ANSWER Find the Mean SOLUTION 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. Mean
ANSWER The mean of the numbers is 0.375 1.5 4 – 3 + ( 4) + (2) + (– 1.5) = 4 = Guided Practice Find the mean of the numbers –3, 4, 2, and – 1.5 . SOLUTION To find the mean, find the sum of the numbers and then divide the sum by 4. = 0.375
Guided Practice Find the mean daily minimum temperature (in degrees Fahrenheit) in Barrow, Alaska, for the first 5 days of February 2004.
ANSWER The mean daily minimum temperature was – 16.8°F. – 3 + (– 20) + (– 21) + (– 22) + (– 18) 5 84 – = 5 – 16.8 = Guided Practice SOLUTION To find the mean daily temperature, find the sum of the minimum temperatures for the 5 days and then divide by 5. Mean =
