Algebra Puzzle – Challenge 36

Challenge:

In a small farm, there are 8 hens, 5 chickens, and 4 roosters. A hen eats 2.5 times of a chick and a rooster eats 1.5 times a hen. If all together eat 4000 seeds per day, how many seeds does a hen eat during one day?

A- 250

B- 280

C- 300

D- 350

E- 400

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Let H represents the number of seeds a hen eats each day, C represents the number of seeds a chicken eats each day and R represents the number of seeds a rooster eats each day. Therefore,
H + C + R = 4205
H = 2.5 C  and R = 1.5 H→R = 1.5 (2.5 C) →R = 3.75 C
Replace the value of H and R in the first equation with their values in the second and third equations:
2.5 C + C + 3.75 C = 4205 → 7.25 C = 4205 → C = 580
H = 2.5 C  → H = 2.5 (580) = 1450
A hen eats 1450 seeds in one day.

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