PUZZLE

A stationery shop sells 8 pens and 2 whiteboard markers for Ghc46.00. If the shop also sells 7 pens and 3 markers for Ghc47.00. What is the cost of one pen and one marker?

ANSWER

Preambles: 8 pens + 2 markers = Ghc46.00; 7 pens + 3 markers = Ghc47.00; 1 pen =? 1 marker =?

Step 1: Denote the price of 1 pen by x and the price of 1 marker by y. 

Step 2: From the preamble, 8x+2y = 46, thus 4x+y = 23…..(equation 1)

Also, 7x+3y=47……(equation 2)

Step 3: From eqn 1, y = 23 – 4x…..(equation 3).

 Substituting this into equation 2, expanding the brackets and solving for x: 7x + 3(23-4x) =47; thus, 7x -12x = 47 -69, therefore,  5x = 22x = 4.4

Step 4: Substitute the value of x into equation 3 to get the value of y. Thus y = 23 – 4(4.4); y = 23 – 17.6. y = 5.4

Therefore, 1 pen costs Ghc4.40 and 1 marker cost Ghc5.40.

CHALLENGE YOURSELF

At these prices how much would it cost to purchase 1 pack of pen and 2 packs of markers? A pack of pens contains 50 pieces of pens and a box of the marker contains twelve pieces of markers.