math

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A man buys 2pens and 4 pencils and gives a hundred rupees note to shop keeper . Shopkeeper ask him to pay Rs10 more to take 4pens and 2pencils. If he bought 2pens and 3pencils how much would the man get back from shopkeeper?

  • math -

    cost of a pen --- x
    cost of a pencil -- y

    2x + 4y ≤ 100

    4x + 2y = (2x+4y) + 10
    2x - 2y = 10
    x-y= 5
    x = 5+y

    then back in 2x+4y<100
    or x+2y ≤ 50
    5+y + 2y ≤ 50
    3y ≤ 45
    y ≤ 15

    cost of 2 pens and 3 pencils
    = 2x + 3y
    = 2(5+y) + 3y
    = 10 + 5y

    there are multiple answers
    Make a chart showing
    x .. y (2x+4y) (4x+2y) (2x+3y)
    20 15 -- 100 -- 110 -- 85 , so change is 15
    19 18 -- 94 --- 104 -- 80 , so change is 20
    etc.
    (If we assume that Rs 100 was the exact amount for 2pens and 4 pencils, then
    20, 15 is the correct answer.)

    e.g.
    If he bought 2 pens at 20 and 4 pencils at 15
    cost would be 100
    Had he bought 4 pens and 2 pencils, cost would be 110 which is 10 more as stated,
    so cost of 2 pens and 3 pencils is 85, resulting in change of 15

    the same can be done for each of the entries in the chart.

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