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. Based on above information, answer the following questions:
38(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. Based on above information, answer the following questions:
38(i) Represent the above situation in terms of a pair of linear equations in two variables.
38(i) Represent the above situation in terms of a pair of linear equations in two variables.
Show Hint
Always simplify your algebraic equations by dividing through by the greatest common divisor of the coefficients.
Working with \(x + 2y = 29\) is far easier than working with \(15x + 30y = 435\).
Working with \(x + 2y = 29\) is far easier than working with \(15x + 30y = 435\).
Updated On: Jun 25, 2026
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Verified By Collegedunia
Correct Answer: 69
Solution and Explanation
Step 1: Understanding the Question:
We are given two different physical exercise sessions with different times spent on two machines (exercise bicycle and double cross walker) and the corresponding total calories burned.
We need to formulate a system of linear equations in two variables to model this situation.
Step 2: Key Formula or Approach: Let \(x\) be the number of calories burned per minute on the exercise bicycle.
Let \(y\) be the number of calories burned per minute on the double cross walker.
We can translate each session into an algebraic equation of the form:
\[ a x + b y = \text{Total Calories} \]
Step 3: Detailed Explanation:
• Let us formulate the first session:
- Time spent on exercise bicycle = 15 minutes.
- Time spent on double cross walker = 30 minutes.
- Total calories burned = 435.
- Equation representing this:
\[ 15x + 30y = 435 \] - Divide the entire equation by 15 to simplify:
\[ x + 2y = 29 \] --- (Equation 1)
• Let us formulate the second session:
- Time spent on exercise bicycle = 30 minutes.
- Time spent on double cross walker = 40 minutes.
- Total calories burned = 690.
- Equation representing this:
\[ 30x + 40y = 690 \] - Divide the entire equation by 10 to simplify:
\[ 3x + 4y = 69 \] --- (Equation 2)
Step 4: Final Answer:
The pair of linear equations is \(x + 2y = 29\) and \(3x + 4y = 69\).
We are given two different physical exercise sessions with different times spent on two machines (exercise bicycle and double cross walker) and the corresponding total calories burned.
We need to formulate a system of linear equations in two variables to model this situation.
Step 2: Key Formula or Approach: Let \(x\) be the number of calories burned per minute on the exercise bicycle.
Let \(y\) be the number of calories burned per minute on the double cross walker.
We can translate each session into an algebraic equation of the form:
\[ a x + b y = \text{Total Calories} \]
Step 3: Detailed Explanation:
• Let us formulate the first session:
- Time spent on exercise bicycle = 15 minutes.
- Time spent on double cross walker = 30 minutes.
- Total calories burned = 435.
- Equation representing this:
\[ 15x + 30y = 435 \] - Divide the entire equation by 15 to simplify:
\[ x + 2y = 29 \] --- (Equation 1)
• Let us formulate the second session:
- Time spent on exercise bicycle = 30 minutes.
- Time spent on double cross walker = 40 minutes.
- Total calories burned = 690.
- Equation representing this:
\[ 30x + 40y = 690 \] - Divide the entire equation by 10 to simplify:
\[ 3x + 4y = 69 \] --- (Equation 2)
Step 4: Final Answer:
The pair of linear equations is \(x + 2y = 29\) and \(3x + 4y = 69\).
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