Question:
Seema daily goes to a park to exercise on machines available there. When Seema spent 15 minutes on exercise bicycle and 30 minutes on double cross walker, she received a message of burning 435 calories on her fitness watch. When she spent 30 minutes on exercise bicycle and 40 minutes on double cross walker, she received a message of burning 690 calories. To find the number of calories burned per minute on each machine, answer the following :
(i)
Represent the above situation in terms of a pair of linear equations in two variables.
Seema daily goes to a park to exercise on machines available there. When Seema spent 15 minutes on exercise bicycle and 30 minutes on double cross walker, she received a message of burning 435 calories on her fitness watch. When she spent 30 minutes on exercise bicycle and 40 minutes on double cross walker, she received a message of burning 690 calories. To find the number of calories burned per minute on each machine, answer the following :
(i) Represent the above situation in terms of a pair of linear equations in two variables.
(i) Represent the above situation in terms of a pair of linear equations in two variables.
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Always simplify equations by dividing by their greatest common divisor (GCD) to make solving them in subsequent parts much easier!
Updated On: Jun 25, 2026
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Correct Answer: 69
Solution and Explanation
Step 1: Understanding the Question:
This is a Case Study question from the chapter Pair of Linear Equations in Two Variables.
We need to model the given scenario into two mathematical linear equations.
Step 2: Key Formula or Approach:
Let the number of calories burned per minute on the exercise bicycle be \(x\).
Let the number of calories burned per minute on the double cross walker be \(y\).
Form equations based on the time spent on each machine and the corresponding total calories burned.
Step 3: Detailed Explanation:
1. Case 1: 15 minutes on exercise bicycle and 30 minutes on double cross walker, burning 435 calories. \[ 15x + 30y = 435 \] Divide the entire equation by 15 to simplify: \[ x + 2y = 29 \quad \text{--- (Equation 1)} \] 2. Case 2: 30 minutes on exercise bicycle and 40 minutes on double cross walker, burning 690 calories. \[ 30x + 40y = 690 \] Divide the entire equation by 10 to simplify: \[ 3x + 4y = 69 \quad \text{--- (Equation 2)} \]
Step 4: Final Answer:
The mathematical representation of the situation is given by the equations: \[ x + 2y = 29 \] \[ 3x + 4y = 69 \]
This is a Case Study question from the chapter Pair of Linear Equations in Two Variables.
We need to model the given scenario into two mathematical linear equations.
Step 2: Key Formula or Approach:
Let the number of calories burned per minute on the exercise bicycle be \(x\).
Let the number of calories burned per minute on the double cross walker be \(y\).
Form equations based on the time spent on each machine and the corresponding total calories burned.
Step 3: Detailed Explanation:
1. Case 1: 15 minutes on exercise bicycle and 30 minutes on double cross walker, burning 435 calories. \[ 15x + 30y = 435 \] Divide the entire equation by 15 to simplify: \[ x + 2y = 29 \quad \text{--- (Equation 1)} \] 2. Case 2: 30 minutes on exercise bicycle and 40 minutes on double cross walker, burning 690 calories. \[ 30x + 40y = 690 \] Divide the entire equation by 10 to simplify: \[ 3x + 4y = 69 \quad \text{--- (Equation 2)} \]
Step 4: Final Answer:
The mathematical representation of the situation is given by the equations: \[ x + 2y = 29 \] \[ 3x + 4y = 69 \]
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