Rational Applications

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Answer Key & Explanations

Rational Applications · Grade 7 · Worksheet 1

1. Ava is tracking the temperature changes in her freezer for a science experiment. At 6:00 AM, the temperature inside the freezer was -16°C. She then opened the freezer door for 30 minutes, causing the temperature to rise by 11°C. After closing the door, the freezer's cooling system worked to lower the temperature by 6°C. Later in the day, she added a warm container of soup, which caused the temperature to increase by 21°C. What is the final temperature inside the freezer? Answer: 10 Solution: Start with the initial temperature: -16°C Temperature rises by 11°C: -16 + 11 = -5°C Temperature decreases by 6°C: -5 - 6 = -11°C Temperature increases by 21°C: -11 + 21 = 10°C The final temperature inside the freezer is 10°C.
   Full step-by-step solution

   Step 1: Start with the initial temperature: -16°C Step 2: Temperature rises by 11°C: -16 + 11 = -5°C Step 3: Temperature decreases by 6°C: -5 - 6 = -11°C Step 4: Temperature increases by 21°C: -11 + 21 = 10°C The final temperature inside the freezer is 10°C.

2. Liam is tracking the elevation of a hot air balloon. The balloon starts at an elevation of 135 meters above sea level. It then descends 220 meters to pick up a passenger. After picking up the passenger, it ascends 175 meters, then descends 95 meters to catch a wind current, and finally ascends 145 meters to reach its cruising altitude. What is the final elevation of the hot air balloon in meters? Answer: 140 Solution: Start at 135 meters. Descend 220 meters: 135 - 220 = -85 meters. Ascend 175 meters: -85 + 175 = 90 meters.
   Full step-by-step solution

   Step 1: Start at 135 meters. Step 2: Descend 220 meters: 135 - 220 = -85 meters. Step 3: Ascend 175 meters: -85 + 175 = 90 meters. Step 4: Descend 95 meters: 90 - 95 = -5 meters. Step 5: Ascend 145 meters: -5 + 145 = 140 meters. The final elevation is 140 meters.

3. Noah's bank account balance was -$126. He deposited $41 and then wrote a check for $56. What is his new balance? Answer: -$141 Solution: Start with the initial balance: -$126. Add the deposit of $41: -126 + 41 = -85. Subtract the check amount of $56: -85 - 56 = -141.
   Full step-by-step solution

   Step 1: Start with the initial balance: -$126. Step 2: Add the deposit of $41: -126 + 41 = -85. Step 3: Subtract the check amount of $56: -85 - 56 = -141. The new balance is -$141.

4. Kaia's bank account balance was -$85. She deposited $120. What is her new balance? Answer: $35 Solution: Start with the initial balance: -$85 Add the deposit: -85 + 120 Calculate: 120 - 85 = 35 The new balance is $35.
   Full step-by-step solution

   Step 1: Start with the initial balance: -$85 Step 2: Add the deposit: -85 + 120 Step 3: Calculate: 120 - 85 = 35 Step 4: The new balance is $35. The answer is $35.

5. (-3/4 + 2/3) × (-12) = ? Answer: 1 Solution: Find a common denominator for -3/4 and 2/3. The least common denominator is 12. Convert -3/4 to -9/12 and 2/3 to 8/12.
   Full step-by-step solution

   Step 1: Find a common denominator for -3/4 and 2/3. The least common denominator is 12. Step 2: Convert -3/4 to -9/12 and 2/3 to 8/12. Step 3: Add the fractions: -9/12 + 8/12 = -1/12. Step 4: Multiply the result by -12: (-1/12) × (-12) = 12/12 = 1. The answer is 1.

6. Noah is tracking the elevation of a drone during a flight. The drone starts at an elevation of -21 meters (below a reference point). It then rises 16 meters, descends 31 meters, and finally rises 26 meters. What is the final elevation of the drone in meters? Answer: -10 Solution: Start at -21 meters. Rise 16 meters: -21 + 16 = -5 meters. Descend 31 meters: -5 + (-31) = -36 meters.
   Full step-by-step solution

   Step 1: Start at -21 meters. Step 2: Rise 16 meters: -21 + 16 = -5 meters. Step 3: Descend 31 meters: -5 + (-31) = -36 meters. Step 4: Rise 26 meters: -36 + 26 = -10 meters. The final elevation of the drone is -10 meters.

7. Emma is planning a road trip from her home to visit her grandparents. The total distance is 315 miles. She drives the first 180 miles at an average speed of 60 miles per hour. After taking a 30-minute break, she drives the remaining distance at an average speed of 45 miles per hour. How many hours, in total, will the entire trip take, including the break? Answer: 6.5 Solution: Distance = 180 miles, Speed = 60 mph Time = Distance ÷ Speed = 180 ÷ 60 = 3 hours Remaining distance = 315 - 180 = 135 miles Speed = 45 mph Time = 135 ÷ 45 = 3 hours 30 minutes = 30 ÷ 60 = 0.5 hours Total time = First segment + Break + Second segment Total time = 3 + 0.5 + 3 = 6.5 hours The…
   Full step-by-step solution

   Step 1: Calculate time for first segment Distance = 180 miles, Speed = 60 mph Time = Distance ÷ Speed = 180 ÷ 60 = 3 hours Step 2: Calculate time for second segment Remaining distance = 315 - 180 = 135 miles Speed = 45 mph Time = 135 ÷ 45 = 3 hours Step 3: Convert break time to hours 30 minutes = 30 ÷ 60 = 0.5 hours Step 4: Calculate total time Total time = First segment + Break + Second segment Total time = 3 + 0.5 + 3 = 6.5 hours The answer is 6.5 hours.