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5 pencils and 7 pens cost ₹50, while 7 pencils and 5 pens cost ₹46. Find the cost of one pencil and one pen.

Mathematics

ScanSolve AI Answer

Step-by-step solution

5 steps

  1. Define variables for the costs.

    Let xx be the cost of one pencil (in ₹).
    Let yy be the cost of one pen (in ₹).

  2. Formulate the system of linear equations based on the given information.

    From the first statement, "5 pencils and 7 pens together cost ₹ 50":

    5x+7y=50(Equation 1)5x + 7y = 50 \quad \text{(Equation 1)}

    From the second statement, "7 pencils and 5 pens together cost ₹ 46":

    7x+5y=46(Equation 2)7x + 5y = 46 \quad \text{(Equation 2)}

  3. Solve the system of equations using the elimination method.

    To eliminate yy, multiply Equation 1 by 5 and Equation 2 by 7:
    Multiply Equation 1 by 5:

    5(5x+7y)=5(50)5(5x + 7y) = 5(50) 25x+35y=250(Equation 3)25x + 35y = 250 \quad \text{(Equation 3)}

    Multiply Equation 2 by 7:

    7(7x+5y)=7(46)7(7x + 5y) = 7(46) 49x+35y=322(Equation 4)49x + 35y = 322 \quad \text{(Equation 4)}

  4. Subtract Equation 3 from Equation 4 to solve for xx.

    (49x+35y)−(25x+35y)=322−250(49x + 35y) - (25x + 35y) = 322 - 250 49x−25x=7249x - 25x = 72 24x=7224x = 72 x=7224x = \frac{72}{24} x=3x = 3

    The cost of one pencil is ₹ 3.

  5. Substitute the value of xx into Equation 1 to solve for yy.

    5(3)+7y=505(3) + 7y = 50 15+7y=5015 + 7y = 50 7y=50−157y = 50 - 15 7y=357y = 35 y=357y = \frac{35}{7} y=5y = 5

    The cost of one pen is ₹ 5.

    The cost of one pencil is ₹ 3.
    The cost of one pen is ₹ 5.

    Cost of one pencil=₹3,Cost of one pen=₹5\boxed{\text{Cost of one pencil} = \text{₹} 3, \text{Cost of one pen} = \text{₹} 5}
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