1. 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)

2. 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.

3. 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

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

5. 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?

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

7. 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

8. 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

9. 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!

10. 4S + 5B = 510
(x2)
2S + 2B = 220 4 4
440 E Q U A L

11. 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.

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

13. 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

14. I want to see the solutions again
I want to see the whole story again