7. In a 'ninety nine' shop all items cost a number of pounds and 99 pence. Susanna spent £65.76.
How many items did she buy?
A 23
B 24
C 65
D 66
E 76
Solution
B Let $k$ be the number of items that Susanna bought. The cost of these is a whole number of pounds and $99 k$ pence, that is, a whole number of pounds less $k$ pence. Susanna spent £65.76, that is, a whole number of pounds less 24 pence. It follows that $k$ pence is a whole number of pounds plus 24 pence. So $k$ is 24 or 124 or 224 or .... . However, since each item costs at least 99 pence and Susanna spent $£ 65.76$ pence, she bought at most 66 items. So $k$ is 24 .