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# Stock-Keeping

"I have three times as many pigs as goats which are a quarter the number of cows which are half my stock."

The inspector retorted "That's not enough information for me to work it out"

"Alright", replied McCoy. "If I sell a goat and a pig and a cow next market day and buy a bull then I will have four times as many pigs as goats".

How many pigs, goats and cows does Farmer McCoy now have?

Solution: 3 goats, 9 pigs and 12 cows

Again we use algebra. We use symbols for the animals and we express the information we have in those symbols and then we can manipulate these statements.

We don’t have to use x,y,z - it’s easier to use P for pigs, G for goats and C for cows.

S for entire stock

Three times as many pigs as goats

P = 3G

Goats are a quarter the number of cows

4G = C

Cows are half of his stock

2C = S

This is not enough information so we find out

If I sell a goat and a pig and a cow next market day and buy a bull then I will have four times as many pigs as goats

That means that

4(G-1) = P-1

4G – 4 = P – 1

4G = P +3

From earlier we know that 3G = P

4G = P + 3

- 3G = P      .

G = 3

There are therefore 3 goats and there are ( P = 3G ) 9 pigs and  (4G = C) 12 cows