Question 1159398
<pre>
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.
<pre>
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:
                                     
                       <u>   6</u> 
                     15)100
                        <u> 90</u>
                         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.

                      <u>  3</u>
                     3)10
                       <u> 9</u>
                        1

So he could get 3 more cakes, or 42+3=45 cakes and have 1 dollar remaining. 

Edwin</pre>