Question

A FARMER SPENDS $1000 AND BUYS 100 ANIMALS. THE PIGS COSTS $100 EACH, THE GOATS $30 AND THE CHICKS $5. THE FARMER BUYS AT LEAST ONE OF EACH ANIMAL, WHAT DOES HE BUY?

Answer 1

p+g+c = 100
100p+30g+5c = 1000

A little checking will show that he bought

94 chickens
1 goat
5 pigs

Answer 2

100 p + 30 g + 5 c = 1,000
p+g+c = 100 so c = 100 - p - g

100 p +30 g +5(100-p-g) = 1,000

95 p +25 g = 500

we know p+g < 100 or we have <1 c
p and g must be integers, no half goats allowed
well 95 times what is a multiple of 25
95 = 5*19
so 95*5 = 19*5*5 =475:)
try 5 pigs

95 p + 25 g = 500
using p = 5
475 + 25 g = 500
g = 1
so
c = 100 - p - g
c = 100 -5 -1 = 94
so
5 pigs, 1 goat, 94 chickens
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check
5*100 + 1*30 + 96*5 = 1,000 whew!