Mathematical Puzzles 

Workings

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.

Workings

Hint
Remember that you have the same number of each coin.

Answer
134 of each coin.

Reasoning
We have equal numbers of 2p, 5p, 10p, and 20p.

And 2p + 5p + 10p + 20p = 37p.

There are 134 lots of 37p in £49.58.

Double-Checking
134 x 37 = 4958.

Workings

Hint
Adults have fewer bones than children.

Answer
Days in a year.

There are usually around 206 bones in an adult human body, and 365 or 366 days in a year.

Workings

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.

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, which is 10 fewer tonnes of chicken feed:

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

Double-Checking
  8 x 4.00 =   £32.00
 12 x 3.00 =   £36.00
 80 x 0.40 =   £32.00
---            ------
100 tonnes =  £100.00