# 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

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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