Samuel, a shopkeeper, bought some Christmas hampers containing bars of soap and bottles of bath oil. A powerpoint presentation by Winston Micallef Head of Department (Mathematics)

Samuel, a shopkeeper, bought some Christmas hampers containing bars of soap and bottles of bath oil. However he did not manage to sell some of them during the Christmas season. So he decided to remove the wrappers and sell the soap and bath oil separately.

4 bars of soap and 5 bottles of bath oil, In the large hamper there were 4 bars of soap and 5 bottles of bath oil, costing Lm5.10

In the small hamper there were 2 bars of soap and 2 bottles of bath oil, costing Lm2.20

How did he do it? Samuel had to find out the prices of one bar of soap and one bottle of bath oil. How did he do it?

cents on each bar of soap He wrote S cents on each bar of soap S S S S S S

cents on each bottle of bath oil and wrote B cents on each bottle of bath oil B B S B S B S B B S B S S

Now he noted the cost of each hamper: 4(S cents) + 5(B cents) = 510 cents 2(S cents) + 2(B cents) = 220 cents 4S + 5B = 510 or in short…. 2S + 2B = 220

problem would be much simpler! 4S + 5B = 510 2S + 2B = 220 Samuel also noted that if he doubled the smaller hamper, the amount of soap would be the same, and his problem would be much simpler!

4S + 5B = 510 (x2) 2S + 2B = 220 4 4 440 E Q U A L

Each bottle of bath oil costs 70 cents. 4S + 5B = 510 (x2) 4 2S + 2B = 220 4 440 By subtracting B = 70 B cents is 70 cents Each bottle of bath oil costs 70 cents.

Each bar of soap costs 40 cents. As ... B cents is 70 cents And … 4S + 5B = 510 Then … 4S + 5(70) = 510 4S + 350 = 510 4S = 510 - 350 4S = 160 S = 40 S cents is 40 cents Each bar of soap costs 40 cents.

Now Samuel can sell his wares because he knows that ... a bar of soap costs 40 cents and a bottle of bath oil costs 70 cents

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