(a) Suppose Amos bought x chickens, and Nathan bought y ducks
Amos’s remaining chickens = 1/2x:
Amos’s remaining ducks = 1/2y - 6:
Nathan’s remaining chickens = 1/2x - 9:
Nathan’s remaining ducks = 1/2y
1/2y - 6 = 1/7 * 1/2x - (1)
1/2y = 1/4 * (1/2x - 9) - (2)
(1) * 2, (2) * 2:
y - 12 = 1/7x - (3)
y = 1/4x - 9/2 - (4)
(4) - (3): 12 = (1/4 - 1/7)x - 9/2 => x = 154 - (5)
y = 1/4 * 154 - 9/2 = 34
So Amos bought 154 chickens.
(b) (1/2 * 154) + (1/2 * 154 - 9) = 154 - 9 = 145
(1/2 * 34 - 6) + (1/2 * 34) = 34 - 6 = 28
So they had 145 chickens and 28 ducks altogether in the end.
Amos bought some chickens and gave half of them to Nathan. Nathan bought some ducks and gave half of them to Amos. Amos sold 6 ducks and Nathan sold 9 chickens. In the end the number of ducks Amos had was 1/7 of the number of his remaining chickens and the number of ducks Nathan had was 1/4 of the number of his remaining chickens.
(a) How many chickens did Amos buy?
(b) How many chickens and ducks did they have altogether in the end?
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