Each empty white square in the grid contains one of the numbers 1, 2, 3, …, 8. Each of the horizontal and vertical equations must be true, and each number must be used exactly once.
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?
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
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, which isn't enough.
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, which isn't enough.
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, which isn't enough.
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 until it works.
