In 1929, Farmer Giles took his animals to market. He had some cows, sheep and chickens to sell. Cows sold for ten pounds each. Sheep sold for one pound each. Chickens were sold for one pound for a brood of eight (they were only sold in whole broods). Farmer Giles had a good day and sold 100 animals for exactly £100. The day did have its down side; he had to sell Daisy, his favourite cow. How many sheep did Farmer Giles sell?

21 sheep

Step-by-step explanation:

100 = x + y + 8z

10x + y + z = 100

x = 1

y + 8z = 99

y + z = 90

x = 2

y + 8z = 98

y + z = 80

x = 3

y + 8z = 97

y + z = 70

x = 4

y + 8z = 96

y + z = 60

x = 5

y + 8z = 95

y + z = 50

x = 6

y + 8z = 94

y + z = 40

x = 7

y + 8z = 93

y + z = 30

7z = 63

z = 9

y = 30 - 9 = 21

x = 7 (7 cows)

y = 21 (21 sheep)

z = 9 (9×8 = 72 chicken)

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3