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Solution for $n$ bananas, where $n$ is the number of bananas you own, and $c$ is the number of bananas the camel can carry:

- For bananas $0 \rightarrow c$ the cost to move a banana is $1$ banana per km.
- For bananas $c+1 \rightarrow 2c$, the cost to move a banana is $3$ bananas per km.
- For bananas $2c+1 \rightarrow 3c$, the cost to move a banana is $5$ bananas per km.
- etc.

This is because, if the camel moves the bananas 1 km at a time, he needs to make two trips for each load beyond his current capacity.

Define $t = \lfloor\frac{n}{c}\rfloor$ Therefore, the total number of miles the camel can reach is:

$$\left(\sum_{k=1}^{t} \frac{c}{2k - 1}\right) + \frac{(n \bmod c)}{2t+1}$$

In particular, plugging in the given $n = 3000$ and $c = 1000$, we have that the camel can travel

$$1000 + 333 + 200 = 1533 \text{ miles}$$

To figure out how many bananas remain for a given distance,

Subtract the extra miles and multiply back at the rate given above.

For the first $1000$ miles, this number is just the distance beyond the total capacity:

$1533 - 1000 = 533$, or 533 bananas.

Solution for $n$ bananas, where $n$ is the number of bananas you own, and $c$ is the number of bananas the camel can carry:

- For bananas $0 \rightarrow c$ the cost to move a banana is $1$ banana per mile.
- For bananas $c+1 \rightarrow 2c$, the cost to move a banana is $3$ bananas per mile.
- For bananas $2c+1 \rightarrow 3c$, the cost to move a banana is $5$ bananas per mile.
- etc.

This is because, if the camel moves the bananas 1 mile at a time, he needs to make two trips for each load beyond his current capacity.

Define $t = \lfloor\frac{n}{c}\rfloor$ Therefore, the total number of miles the camel can reach is:

$$\left(\sum_{k=1}^{t} \frac{c}{2k - 1}\right) + \frac{(n \bmod c)}{2t+1}$$

In particular, plugging in the given $n = 3000$ and $c = 1000$, we have that the camel can travel

$$1000 + 333 + 200 = 1533 \text{ miles}$$

To figure out how many bananas remain for a given distance,

Subtract the extra miles and multiply back at the rate given above.

For the first $1000$ miles, this number is just the distance beyond the total capacity:

$1533 - 1000 = 533$, or 533 bananas.

Solution for $n$ bananas, where $n$ is the number of bananas you own, and $c$ is the number of bananas the camel can carry:

• For bananas $0 \rightarrow c$ the cost to move a banana is $1$ banana per km.
• For bananas $c+1 \rightarrow 2c$, the cost to move a banana is $3$ bananas per km.
• For bananas $2c+1 \rightarrow 3c$, the cost to move a banana is $5$ bananas per km.
• etc.

This is because, if the camel moves the bananas 1 km at a time, he needs to make two trips for each load beyond his current capacity.

Define $t = \lfloor\frac{n}{c}\rfloor$ Therefore, the total number of miles the camel can reach is:

$$ \left(\sum_{k=1}^{t} \frac{c}{2k - 1}\right) + \frac{(n \bmod c)}{2t+1} $$

In particular, plugging in the given $n = 3000$ and $c = 1000$, we have that the camel can travel

$$ 1000 + 333 + 200 = 1533 \text{ miles} $$

To figure out how many bananas remain for a given distance, subtract the extra miles and multiply back at the rate given above.

For the first $1000$ miles, this number is just the distance beyond the total capacity $1533 - 1000 = 533$, or 533 bananas.

Solution for $n$ bananas, where $n$ is the number of bananas you own, and $c$ is the number of bananas the camel can carry:

- For bananas $0 \rightarrow c$ the cost to move a banana is $1$ banana per km.
- For bananas $c+1 \rightarrow 2c$, the cost to move a banana is $3$ bananas per km.
- For bananas $2c+1 \rightarrow 3c$, the cost to move a banana is $5$ bananas per km.
- etc.

This is because, if the camel moves the bananas 1 km at a time, he needs to make two trips for each load beyond his current capacity.

Define $t = \lfloor\frac{n}{c}\rfloor$ Therefore, the total number of miles the camel can reach is:

$$\left(\sum_{k=1}^{t} \frac{c}{2k - 1}\right) + \frac{(n \bmod c)}{2t+1}$$

In particular, plugging in the given $n = 3000$ and $c = 1000$, we have that the camel can travel

$$1000 + 333 + 200 = 1533 \text{ miles}$$

To figure out how many bananas remain for a given distance,

Subtract the extra miles and multiply back at the rate given above.

For the first $1000$ miles, this number is just the distance beyond the total capacity:

$1533 - 1000 = 533$, or 533 bananas.

Solution in $n$ bananas, where $n$ is the number of bananas you own, and $c$ is the number of bananas the camel can carry.

Solution:

• For bananas $0 \rightarrow c$ the cost to move a banana is $1$ banana per km.
• For bananas $c+1 \rightarrow 2c$, the cost to move a banana is $3$ bananas per km.
• For bananas $2c+1 \rightarrow 3c$, the cost to move a banana is $5$ bananas per km.
• etc.

This is because, if the camel moves the bananas 1 km at a time, he needs to make two trips for each load beyond his current capacity.

Define $t = \lfloor\frac{n}{c}\rfloor$ Therefore, the total number of miles the camel can reach is:

$$ \left(\sum_{k=1}^{t} \frac{c}{2k - 1}\right) + \frac{(n \bmod c)}{2t+1} $$

In specific, plugging in the given $n = 3000$ and $c = 1000$, we have the camel able to travel:

$$ 1000 + 333 + 200 = 1533 \text{ miles} $$

To figure out how many bananas remain for a given distance, subtract the extra miles and multiply back at the rate given above.

For the first $1000$ miles, this number is just the distance beyond the total capacity $1533 - 1000 = 533$, or 533 bananas.

Solution for $n$ bananas, where $n$ is the number of bananas you own, and $c$ is the number of bananas the camel can carry:

• For bananas $0 \rightarrow c$ the cost to move a banana is $1$ banana per km.
• For bananas $c+1 \rightarrow 2c$, the cost to move a banana is $3$ bananas per km.
• For bananas $2c+1 \rightarrow 3c$, the cost to move a banana is $5$ bananas per km.
• etc.

This is because, if the camel moves the bananas 1 km at a time, he needs to make two trips for each load beyond his current capacity.

Define $t = \lfloor\frac{n}{c}\rfloor$ Therefore, the total number of miles the camel can reach is:

$$ \left(\sum_{k=1}^{t} \frac{c}{2k - 1}\right) + \frac{(n \bmod c)}{2t+1} $$

In particular, plugging in the given $n = 3000$ and $c = 1000$, we have that the camel can travel

$$ 1000 + 333 + 200 = 1533 \text{ miles} $$

To figure out how many bananas remain for a given distance, subtract the extra miles and multiply back at the rate given above.

For the first $1000$ miles, this number is just the distance beyond the total capacity $1533 - 1000 = 533$, or 533 bananas.