Two step equations with negative numbers worksheet :
Worksheet on two step equations with negative numbers is much useful to the students who would like to practice solving word problems in Algebra.
1. To convert a temperature from degrees Fahrenheit to degrees Celsius, first subtract 32. Then multiply the result by 5/9. An outdoor thermometer showed a temperature of -10 °C. What was the temperature in degrees Fahrenheit ?
2. What is the temperature in degrees Fahrenheit of a freezer kept at -20 °C ?
3. An airplane flies at an altitude of 38,000 feet. As it nears the airport, the plane begins to descend at a rate of 600 feet per minute. At this rate, how many minutes will the plane take to descend to 18,800 feet ?
4. Jenny earned 92 of a possible 120 points on a test. She lost 4 points for each incorrect answer. How many incorrect answers did she have ?
Problem 1 :
To convert a temperature from degrees Fahrenheit to degrees Celsius, first subtract 32. Then multiply the result by 5/9. An outdoor thermometer showed a temperature of -10 °C. What was the temperature in degrees Fahrenheit ?
Solution :
Step 1 :
Let x represent the temperature in degrees Fahrenheit.
Write an equation.
-10 = (5/9).(x - 32)
Step 2 :
Solve the equation.
Multiply both sides by 9/5
(9/5).(-10) = (9/5).(5/9).(x - 32)
-18 = x - 32
Add 32 to both sides.
-18 + 32 = x - 32 + 32
14 = x
Hence, the temperature was 14 degrees Fahrenheit.
Problem 2 :
What is the temperature in degrees Fahrenheit of a freezer kept at -20 °C?
Solution :
Step 1 :
Let x represent the temperature in degrees Fahrenheit.
Write an equation.
-20 = (5/9).(x - 32)
Step 2 :
Solve the equation.
Multiply both sides by 9/5
(9/5).(-20) = (9/5).(5/9).(x - 32)
-36 = x - 32
Add 32 to both sides.
-36 + 32 = x - 32 + 32
-4 = x
Hence, the temperature was -4 degrees Fahrenheit.
Problem 3 :
An airplane flies at an altitude of 38,000 feet. As it nears the airport, the plane begins to descend at a rate of 600 feet per minute. At this rate, how many minutes will the plane take to descend to 18,800 feet ?
Solution :
Step 1 :
Let m represent the number of minutes. Write an equation.
38,000 - 600m = 18,800
Step 2 :
Subtract 38,000 from both sides.
(38,000 - 600m) - 38,000 = 18,800 - 38,000
-600m = -19,200
Divide both sides by -600
(-600m)/(-600) = (-19,200)/(-600)
m = 32
Hence, the plane will take 32 minutes to descend to 18,800 feet.
Problem 4 :
Jenny earned 92 of a possible 120 points on a test. She lost 4 points for each incorrect answer. How many incorrect answers did she have?
Solution :
Step 1 :
Let m represent the number of incorrect answers. Write an equation.
120 - 4m = 92
Step 2 :
Subtract 120 from both sides.
(120 - 4m) - 120 = 92 - 120
-4m = -28
Divide both sides by -4
(-4m)/(-4) = (-28)/(-4)
m = 7
Hence, Jenny had 7 incorrect answers.
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