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Two Pens and Three Pencils Cost 86. Four Pens and a Pencil Cost 112. Find the Cost of a Pen and that of a Pencil?

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Explanation

  • Two pens and three pencils cost 86.
  • Four pens and a pencil cost 112.
  • Let suppose “p” shows pen and “c” shows pencil.

2p + 3c = 86       (as 2 pens and 3 pencils cost 86).

4p + c = 112       (as 4 pens and a pencil cost 112).

By solving, these two equations simultaneously p = 25 and c = 12 which are required answers.

To Find

Price of a pen = ?

Price of a pencil = ?

Solution

Let suppose “p” shows pen and “c” shows pencil.

Now, according to given condition;

2p + 3c = 86 _______ (i)

4p + c = 112 _______ (ii)

Multiplying equation (i) with 2; we have

4p + 6c = 172 ______ (iii)

Now, subtracting equation (ii) from (iii)

(4p + 6c) – (4p + c) = 172 – 112

4p + 6c – 4p – c = 60

5c = 60

c = 12 putting this value in equation (i)

2p + 3(12) = 86

2p + 36 = 86

2p = 86 – 36

2p = 50

p = 25

so; price of pen = 25 and pencil = 12 answer

Conclusion

Two pens and three pencils cost 86. Four pens and a pencil cost 112. The cost of a pen and that of a pencil will be 25 and 12 respectively.

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