At a zoo, 3 pandas eat a total of 181 1/2 pounds of bamboo shoots each day. The male panda eats 3 times as much as the baby. The female eats twice as much as the baby. How many pounds of bamboo shoots does the female panda eat? Show work.
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To find out how many pounds of bamboo shoots the female panda eats, we need to first find out how much the baby panda eats.
Let's assume the baby panda eats x pounds of bamboo shoots each day.
According to the problem, the male panda eats 3 times as much as the baby, so the male panda eats 3x pounds of bamboo shoots each day.
Similarly, the female panda eats twice as much as the baby, so the female panda eats 2x pounds of bamboo shoots each day.
Now, we can set up an equation to represent the total amount of bamboo shoots consumed by the pandas each day:
Baby's bamboo shoots + Male's bamboo shoots + Female's bamboo shoots = Total bamboo shoots
x + 3x + 2x = 181 1/2
To simplify the equation, we combine like terms on the left side:
6x = 181 1/2
Next, we convert 181 1/2 to an improper fraction:
6x = 363/2
To solve for x, we divide both sides of the equation by 6:
x = (363/2) ÷ 6
x = (363/2) × (1/6)
x = 363/12
x = 30 1/4
So, the baby panda eats 30 1/4 pounds of bamboo shoots each day.
Now, we can find out how much the female panda eats:
Female's bamboo shoots = 2x
Female's bamboo shoots = 2 × (30 1/4)
Female's bamboo shoots = 60 1/2
Therefore, the female panda eats 60 1/2 pounds of bamboo shoots each day.
Baby eats X Lbs.
Male eats 3x Lbs.
Female eats 2x Lbs.
x + 2x + 3x = 181.5 Lbs. Solve for x.