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?

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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.