At my local farmer's merchant, you can buy chicken feed for £4 per tonne, pig feed for £3 per tonne, and cattle feed for 40p 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 must the number of tonnes of cattle feed be a multiple of?

Answer

I bought 8 tonnes of chicken feed, 12 tonnes of pig feed, and 80 tonnes of cattle feed.

Reasoning

8 x 4.00 = 32.00

12 x 3.00 = 36.00

80 x 0.40 = 32.00

100 tonnes = £100.00

The number of tonnes of cattle feed must be a multiple of 5, because we need to have a whole number of pounds (5 x 0.40).

If all 100 tonnes was cattle feed the cost would have been £40, which isn't enough.

If 95 tonnes was cattle feed the cost would have been £38, and the remaining 5 tonnes of (the most expensive) chicken feed at £20, gives a total of £58.

If 90 tonnes was cattle feed the cost would have been £36, and the remaining 10 tonnes of (the most expensive) chicken feed at £40, gives a total of £76.

If 85 tonnes was cattle feed the cost would have been £34, and the remaining 15 tonnes of (the most expensive) chicken feed at £60, gives a total of £94.

If 80 tonnes was cattle feed the cost would have been £32, and the remaining 20 tonnes of (the most expensive) chicken feed at £80, gives a total of £112. So, this might be a possible answer...

We need 20 tonnes of chicken feed and pig feed to equal £68, so let's reduce the chicken feed tonnage until it works.

20 chicken + 0 pig = 80 + 0 = £80

19 chicken + 1 pig = 76 + 3 = £79

18 chicken + 2 pig = 72 + 6 = £78...

We can see it's coming down 1 at a time, so we need to come down to a total of £68:

8 chicken + 12 pig = 32 + 36 = 68. As required.