### Brain Teasers

# Rotten Apples

Mad Ade's Father (Mr Mad Ade snr) asked young Mad Ade to go shopping for apples one day. He gives young Mad Ade exactly £1 (100 pence) and instructs him that he must spend all of it and buy exactly 100 apples from the market.

Now, the market sells three kinds of apples. Good apples are priced at 10 pence, Average apples at 5 pence and Rotten apples at 0.5 pence.

It does not matter what type of apples young Mad Ade buys, as long as there is 100 in total. How many of each apple must young Mad Ade buy in order to fulfil his father's (Mr Mad Ade snr) instructions?

Now, the market sells three kinds of apples. Good apples are priced at 10 pence, Average apples at 5 pence and Rotten apples at 0.5 pence.

It does not matter what type of apples young Mad Ade buys, as long as there is 100 in total. How many of each apple must young Mad Ade buy in order to fulfil his father's (Mr Mad Ade snr) instructions?

### Answer

Assume that young Mad Ade will buy total of X apples of 10 pence each, Y apples of 5 pence each and Z apples of 0.5 pence each.As young Mad Ade must buy 100 apples,

X + Y + Z = 100 ----------I

Also, the total price must be 100 pence,

10 * X + 5 * Y + 0.5 * Z = 100

20 * X + 10 * Y + Z = 200 ----------II

Subtracting equation I from equation II,

19 * X + 9 * Y = 100

It is obvious that values of X, Y and Z are integers. So using trial and error, X = 1 and Y = 9

Using values of X and Y, then Z = 90

1 Good apple = 10 pence

9 Average apple = 45 pence

90 rotten apples = 45 pence

Hence, total of 100 apples for 100 pence.

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