5 pens and 6 pencils together cost Rs 9 and 3 pens and 2 pencils cost Rs 5. Find the cost of 1 pen and 1 pencil.


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Let the cost of 1 pen be ‘a’ and the cost of 1 pencil be ‘b’.

Given,

5 pens and 6 pencils together cost Rs 9.

5a + 6b = 9 --------- (1)

Given,

3 pens and 2 pencils cost Rs 5.

3a + 2b = 5 -------- (2)

Multiplying eq2 by 3 and subtracting eq1 from it.

3(3a + 2b) - (5a + 6b ) = 5(3) - 9

⇒ 9a + 6b – 5a – 6b = 15 – 9

⇒ 4a = 6

⇒ a = 3/2

Substituting value of 'a' in (1)

⇒ 15/2 + 6b = 9

⇒ 6b = 3/2

⇒ b = 1/4

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