Mathematics5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and a pen respectively.

5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and a pen respectively.


  1. A
    Rs. 4 and Rs. 6
  2. B
    Rs. 3 and Rs. 5
  3. C
    Rs. 2 and Rs. 6
  4. D
    Rs. 3 and Rs. 4 

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    Solution:

    We have been given that 5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46.
    We need to find the cost of one pencil and a pen.
    Let the cost of one pencil be x and the cost of one pen be y.
    According to the question, the algebraic equations are represented as,
    5x+7y=50
    7x+5y=46
    For the equation 5x+7y=50 put x=-4 to obtain the value of y.
    5x+7y=50
    ⇒5-4+7y=50
    ⇒-20+7y=50
    ⇒7y=70
    ⇒y=10
    For the equation 5x+7y=50 put y=0 to obtain the value of x.
    5x+7y=50
    ⇒5x+70=50
    ⇒5x=50
    ⇒x=10
    So, the coordinates of the line equation 5x+7y=50 are (-4, 10) and (10, 0).
    For the second equation 7x+5y=46 put x=-2 to obtain the value of y.
    7x+5y=46
    ⇒7-2+5y=46
    ⇒-14+5y=46
    ⇒5y=60
    ⇒y=12
     Put y=5 in the equation 7x+5y=46 to obtain the value of x.
    7x+5y=46
    ⇒7x+55=46
    ⇒7x+25=46
    ⇒7x=21
    ⇒x=3
    So, the coordinates of the line equation 7x+5y=46 are (-2,12) and (3,5).
    Plot the graph of the line 5x+7y=50 using the table below:

    x

    -4

    10

    y

    10

    0

    Plot the graph of the line 7x+5y=46 using the table below:

    x

    -2

    3

    y

    12

    5

    The graph of the given lines is,
    From the graph, the two lines 5x+7y=50  and 7x+5y=46 are intersecting at the point (3, 5).
    Hence, the cost of one pencil is Rs. 3 and the cost of one pen is Rs. 5.
    Hence, option 2 is correct.
     
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