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NCERT Solutions · Class 9 Mathematics Two Variables, One Line

42 questions · 42 still being checked

Exercise Set 13.4 1–3 (part 4 of 7)

  1. Given below are some everyday situations. Construct a pair of linear equations in two variables for each situation:

    Exercise 1

    On two different days a family buys movie tickets and snack boxes. Let the cost of one movie ticket be ₹ x\displaystyle x and the cost of one snack box be ₹y. Frame a pair of linear equations in x\displaystyle x and y\displaystyle y to represent the following situations:
    (i)
    On the first day, the family buys 2\displaystyle 2 movie tickets and 3\displaystyle 3 snack boxes for ₹850.
    (ii)
    On the second day, the family buys 4\displaystyle 4 movie tickets and 1\displaystyle 1 snack box for ₹1100.

    Not cross-checked

    This solution has not been cross-checked against the answer printed in NCERT.

    Cost of one ticket \(\displaystyle = ₹x \), cost of one snack box \(\displaystyle = ₹y \).(i) Day $\displaystyle 1$: \(\displaystyle 2 \) tickets and \(\displaystyle 3 \) snack boxes. \[2x + 3y = 850 \](ii) Day $\displaystyle 2$: \(\displaystyle 4 \) tickets and \(\displaystyle 1 \) snack box. \[4x + y = 1100 \]Answer: \(\displaystyle 2x + 3y = 850 \) and \(\displaystyle 4x + y = 1100 \)

  2. Exercise 2

    Two friends, Sahil and Meena, travelled by taxi. Let the fixed charge for one taxi trip be ₹ x\displaystyle x and the additional charge per kilometre be ₹y. Frame a pair of linear equations in x\displaystyle x and y\displaystyle y to represent the following situation:
    (i)
    Sahil travelled 6\displaystyle 6 km and paid a total fare of ₹122.
    (ii)
    Meena travelled 8\displaystyle 8 km and paid a total fare of ₹160.

    Not cross-checked

    This solution has not been cross-checked against the answer printed in NCERT.

    For a trip of \(\displaystyle d \) km, fare \(\displaystyle = \) fixed charge \(\displaystyle + \) (charge per km) \(\displaystyle \times d \). \[x + d\,y = \text{fare} \](i) Sahil: \(\displaystyle d = 6 \), fare \(\displaystyle ₹122 \). \[x + 6y = 122 \](ii) Meena: \(\displaystyle d = 8 \), fare \(\displaystyle ₹160 \). \[x + 8y = 160 \]Answer: \(\displaystyle x + 6y = 122 \) and \(\displaystyle x + 8y = 160 \)

  3. Exercise 3

    In a sports meet, tickets for adults cost ₹150\displaystyle 150 each and tickets for children cost ₹100\displaystyle 100 each. A total of 200\displaystyle 200 people attended the meet, and the total amount collected from ticket sales was ₹25\displaystyle 25,000. (Let the number of adult tickets sold be x\displaystyle x and the number of children's tickets sold be y.) Frame a pair of linear equations in x\displaystyle x and y\displaystyle y to represent this situation.

    Not cross-checked

    This solution has not been cross-checked against the answer printed in NCERT.

    \(\displaystyle x \) adult tickets and \(\displaystyle y \) children's tickets are sold.Number of people: \[x + y = 200 \] Amount collected, at \(\displaystyle ₹150 \) per adult and \(\displaystyle ₹100 \) per child: \[150x + 100y = 25000 \] Dividing the second equation by \(\displaystyle 50 \): \[3x + 2y = 500 \]Answer: \(\displaystyle x + y = 200 \) and \(\displaystyle 150x + 100y = 25000 \) (equivalently \(\displaystyle 3x + 2y = 500 \))