At my local farmer's merchant, you can buy chicken feed for 15c per tonne, pig feed for $1.25 per tonne, and cattle feed for 40c per tonne. The feed can only be purchased by the tonne, and part tonnes aren't sold.
Last week I bought some animal feed, and luckily I managed to buy exactly 100 tonnes for exactly $100. How much of each feed did I buy?
Puzzle Copyright © Kevin Stone
	
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	Hint
What are the maximum and minimum tonnes of pig feed I could have bought?
 
	 
	
	
Answer
I bought 15 tonnes of chicken feed, 75 tonnes of pig feed, and 10 tonnes of cattle feed.
 15 x 0.15 =    2.25
 75 x 1.25 =   93.75
 10 x 0.40 =    4.00
100 tonnes = $100.00
A possible solution method follows …
I couldn't have bought 80 tonnes of pig feed because this would have cost the full $100.00, but I wouldn't have then had 100 tonnes in total.
Similarly, 70 tonnes of pig feed would have been too few, as this would cost $87.50 and even the remaining 30 tonnes all being cattle feed wouldn't have reached the required $100.00.
So, let's try 71 tonnes of pig feed = $88.75:
   plus 1 x chicken feed + 28 x cattle feed is over $100.00
   or   2 x chicken feed + 27 x cattle feed is under $100.00
   so 71 tonnes of pig feed doesn't work.
Let's try 72 tonnes … and so on.
We soon get to 75 tonnes of pig feed and find the answer.
 
	 
	
	 
	
	 
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