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We know that at a zoo, 3 pandas eat a total of [tex]\(181 \frac{1}{2}\)[/tex] pounds of bamboo shoots each day. We are tasked with finding out how many pounds the female panda eats. Let's break down the information:
1. The total amount of bamboo shoots eaten by all pandas together is [tex]\(181 \frac{1}{2}\)[/tex] pounds, which is equivalent to 181.5 pounds.
2. We need to determine how much bamboo each panda eats. The problem tells us:
- The male panda eats 3 times as much bamboo as the baby panda.
- The female panda eats twice as much bamboo as the baby panda.
Let's denote the amount of bamboo eaten by the baby panda as [tex]\(x\)[/tex] pounds.
3. Therefore, the amount of bamboo eaten by the male panda is [tex]\(3x\)[/tex] pounds.
4. The amount of bamboo eaten by the female panda is [tex]\(2x\)[/tex] pounds.
Now we can set up an equation based on the total bamboo eaten:
[tex]\[
x + 3x + 2x = 181.5
\][/tex]
By combining the terms on the left side, we get:
[tex]\[
6x = 181.5
\][/tex]
Next, solve for [tex]\(x\)[/tex] by dividing both sides of the equation by 6:
[tex]\[
x = \frac{181.5}{6} = 30.25
\][/tex]
So, the baby panda eats [tex]\(30.25\)[/tex] pounds of bamboo each day.
We need to find out how much the female panda eats. Since the female panda eats twice as much as the baby panda:
[tex]\[
\text{Amount eaten by the female panda} = 2 \times 30.25 = 60.5 \text{ pounds}
\][/tex]
Therefore, the female panda eats 60.5 pounds of bamboo shoots each day.
We know that at a zoo, 3 pandas eat a total of [tex]\(181 \frac{1}{2}\)[/tex] pounds of bamboo shoots each day. We are tasked with finding out how many pounds the female panda eats. Let's break down the information:
1. The total amount of bamboo shoots eaten by all pandas together is [tex]\(181 \frac{1}{2}\)[/tex] pounds, which is equivalent to 181.5 pounds.
2. We need to determine how much bamboo each panda eats. The problem tells us:
- The male panda eats 3 times as much bamboo as the baby panda.
- The female panda eats twice as much bamboo as the baby panda.
Let's denote the amount of bamboo eaten by the baby panda as [tex]\(x\)[/tex] pounds.
3. Therefore, the amount of bamboo eaten by the male panda is [tex]\(3x\)[/tex] pounds.
4. The amount of bamboo eaten by the female panda is [tex]\(2x\)[/tex] pounds.
Now we can set up an equation based on the total bamboo eaten:
[tex]\[
x + 3x + 2x = 181.5
\][/tex]
By combining the terms on the left side, we get:
[tex]\[
6x = 181.5
\][/tex]
Next, solve for [tex]\(x\)[/tex] by dividing both sides of the equation by 6:
[tex]\[
x = \frac{181.5}{6} = 30.25
\][/tex]
So, the baby panda eats [tex]\(30.25\)[/tex] pounds of bamboo each day.
We need to find out how much the female panda eats. Since the female panda eats twice as much as the baby panda:
[tex]\[
\text{Amount eaten by the female panda} = 2 \times 30.25 = 60.5 \text{ pounds}
\][/tex]
Therefore, the female panda eats 60.5 pounds of bamboo shoots each day.
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