Answer
Humpty Dumpty sat on a wall.
Humpty Dumpty had a great fall.
All the king's horses and all the king's men
Couldn't put Humpty together again.
??
Puzzle 528
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?
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.
