John had 100 dollars to spend on cakes. The shop had an ad with the following
prices.
3 dollars a cake
Buy 5 cakes get 2 for free.
What is most number of cakes that he can buy with all his money.
First of all, this is the old "buy some and get some free" trick which has been
played on customers for many years. [The one I see most often is "Buy 3 tires
at the regular price and get the 4th tire free".
So let's eliminate the trick played. If he buys 5 cakes for $15 and get 2 free,
the bottom line is that he's paid $15 and gotten 7 cakes. So the merchant
might as well have said "$3 a cake, or 7 cakes for $15".
So we divide $15 into $100 to see how many groups of 7 cakes he could get:
6
15)100
90
10
That would give him 6∙7 = 42 cakes. That remainder of 10 tells us that he would
have $10 remaining. That's not enough money remaining to buy 5 more cakes at $3
a cake, so he could not get any free cakes. But he could still use it to get a
few more cakes even if he couldn't get any free ones.
3
3)10
9
1
So he could get 3 more cakes, or 42+3=45 cakes and have 1 dollar remaining.
Edwin
