234 Unit 6 Problem solving: further techniques
• This chapter has shown how knowledge
of a few relatively simple mathematical
techniques can make the solution of some
problem-solving questions quicker and
more reliable.
• Percentage calculations can be simplified
by replacing the percentages with real
numbers.• The use of algebra, lowest common
factors and multiples, and permutations
and combinations can aid the finding of
methods of solution and shorten the work
required for some problems.Summary
3 From my boat at sea I can see three
lighthouses, which flash with different
patterns:• Lighthouse A flashes 1 second on, 2
seconds off, 1 second on, 1 second off,
then repeats.
• Lighthouse B flashes 1 second on, 3
seconds off, 1 second on, 2 seconds
off, 1 second on, 3 seconds off, then
repeats.
• Lighthouse C flashes 2 seconds on, 1
second off, 1 second on, 2 seconds off,
then repeats.
They have all just started their cycles at
the same time. When do they next all go
on at the same time?
4 Four friends have a photograph taken with
them all throwing their graduation hats in
the air. Afterwards they pick up the hats
and find they all have the wrong hat. How
many different combinations of picking up
the hats are there? In how many of these
combinations do they all have the wrong hat?Answers and comments are on pages 333–34.1 Rita has a small shop. 40% of the money
she receives from selling cornflakes is
profit. Next week she is having a sale and
is selling cornflakes at three packets for
the price of two. What percentage profit
will she make on cornflakes sold under this
offer?
2 At my local baker’s, the price of bread rolls
is 25¢ and I went with exactly the right
money to buy the number I needed. When
I got there, I found they had an offer giving
5¢ off all rolls if you bought eight or more.
Consequently, I found I could buy three
more for exactly the same money. How
many was I originally going to buy?End-of-chapter assignments