Question

At a pencil sale, all pens are sold at one price and all pencils are another price. If 3 pens and 2 pens are sold for 47c, while 2 pens and 3 pencils are sold for 38c, what is the cost of a set of one pen and one pencil in cents?

Answer 1

Given:

3 pens and 2 pens are sold for 47 cents

2 pens and 3 pencils are sold for 38 cents

To find:

The cost of a set of one pen and one pencil in cents

Solution:

Let's assume,

"x" → the price of one pen

"y" → the price of one pencil

So, according to the question, we can form 2 equations as follows:

3x + 2y = 0.47 ....... (i)

and

2x + 3y = 0.38 ....... (ii)

Now, we will multiply eq. (i) by 2 and eq. (ii) by 3 and then subtract the equations to find the value of y first.

6x + 4y = 0.94

6x + 9y = 1.14

-     -         -

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    -5y = -0.2

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∴ y = $\frac{0.2}{5}$ = 0.04 = 4 cents

On substituting y = 0.04 in eq. (i), we get

3x + (2 × 0.04) = 0.47

⇒ 3x = 0.47 - 0.08

⇒ 3x = 0.39

⇒ x = $\frac{0.39}{3}$

⇒ x = 0.13

⇒ x = 13 cents

∴ The cost of a set of 1 pen and 1 pencil = 13 + 4 = 17 cents

Thus, the cost of a set of one pen and one pencil in cents is 17 cents.

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