<Question>
Navin from Mauritius, Luka from Croatia, and Ian from Botswana are chatting in the lobby of a youth hostel discussing their part-time jobs. They learn that Navin makes 160 rupee per hour, Luka makes 25 kuna per hour, and Ian makes 34 pula per hour. If one US dollar is equivalent to 32.35 Mauritius rupee, 5.18 Croatian kuna, and 6.95 Botswana pula, who would earn the most after working an eight-hour day?
</Question>

<think>
<Plan_1>
Okay, let's see. So Navin, Luka, and Ian are comparing their earnings from their part-time jobs. The question is asking who earns the most after working eight hours. Hmm. Alright, let's break this down step by step.

First, I need to figure out how much each person makes in their respective currencies after working eight hours. Then, convert those amounts into a common currency so we can compare them. The problem gives exchange rates for each person's currency to US dollars, so converting everything to USD makes sense.

<prompt_1.1> Identify the necessary steps to determine who earns the most after working eight hours. </prompt_1.1>
</Plan_1>

<Execution_1>
<execution_1.1>
Let me start with Navin from Mauritius. He makes 160 rupees per hour. If he works eight hours, his total earnings would be 160 multiplied by 8. Let me calculate that: 160 * 8 = 1,280 rupees. Now, the exchange rate is 1 US dollar = 32.35 Mauritius rupees. So to find out how many dollars that is, I divide his total rupees by the exchange rate. So 1,280 / 32.35. Let me compute that.
</execution_1.1>
</Execution_1>

<Plan_2>
Based on execution_1.1:
Let me do 1,280 divided by 32.35.

First, approximate: 32.35 * 40 = 1,294.

<prompt_2.1> Calculate Navin's earnings in USD using the given exchange rate. </prompt_2.1>

Next, Luka from Croatia. He makes 25 kuna per hour. Eight hours would be 25 * 8 = 200 kuna. The exchange rate is 1 USD = 5.18 kuna. So to convert kuna to USD, divide by 5.18. So 200 / 5.18. Let's calculate that.

<prompt_2.2> Calculate Luka's earnings in USD using the given exchange rate. </prompt_2.2>

Now Ian from Botswana. He makes 34 pula per hour. Eight hours: 34 * 8 = 272 pula. Exchange rate is 1 USD = 6.95 pula. So divide 272 by 6.95.

<prompt_2.3> Calculate Ian's earnings in USD using the given exchange rate. </prompt_2.3>
</Plan_2>

<Execution_2>
<execution_2.1>
So that's a bit less than 40. Since 32.35 * 40 is 1,294, which is 14 more than 1,280. So maybe 39.25? Wait, let me do it properly. 1,280 ÷ 32.35. Let's compute this division step by step.

32.35 goes into 128 how many times? 32.35*3=97.05, 32.35*4=129.4 which is too much. So 3 times. 128 - 97.05 = 30.95. Bring down the 0, making 309.5. 32.35*9=291.15. Subtract that from 309.5: 309.5 - 291.15 = 18.35. Bring down the next 0, making 183.5. 32.35*5=161.75. Subtract: 183.5 - 161.75 = 21.75. Bring down a 0, making 217.5. 32.35*6=194.1. Subtract: 217.5 - 194.1 = 23.4. So it's approximately 39.25. Let me check with calculator steps. 32.35 * 39 = 1,259.65. Then 1,280 - 1,259.65 = 20.35. 20.35 / 32.35 ≈ 0.629. So total is approximately 39.629. So around 39.63 USD. Let me just use precise calculation. Maybe use a calculator method here. But for the sake of time, let's say approximately $39.63.
</execution_2.1>

<execution_2.2>
5.18 * 38 = 196.84. 5.18 * 38.5 = 196.84 + (5.18 * 0.5) = 196.84 + 2.59 = 199.43. Close to 200. So 38.5 gives 199.43, so 200 / 5.18 is approximately 38.54. Let's say approximately $38.54.
</execution_2.2>

<execution_2.3>
Let me compute that.
</execution_2.3>
</Execution_2>

<Plan_3>
Based on execution_2.1, execution_2.2:
Wait, let me check that again. Maybe compute more accurately.

<prompt_3.1> Compare the USD earnings of Navin, Luka, and Ian to determine who earns the most. </prompt_3.1>
-----

Based on execution_2.3:
Let's do 272 ÷ 6.95.

6.95*39=269.05. 272 -269.05=2.95. 2.95/6.95≈0.424.

<prompt_3.2> Verify Ian's USD earnings calculation and confirm the final result. </prompt_3.2>
</Plan_3>

<Execution_3>
<execution_3.1>
272 divided by 6.95. Let's see. 6.95 * 39 = 269.05. Then 272 - 269.05 = 2.95. So 2.95 / 6.95 ≈ 0.424. So total is 39 + 0.424 ≈ 39.424. So approximately $39.42.

So summarizing:

Navin: ~$39.63
Luka: ~$38.54
Ian: ~$39.42
</execution_3.1>

<execution_3.2>
So total is 39.424. So approximately 39.42 USD.

So summarizing:

Navin: ~39.63 USD

Luka: ~38.54 USD

Ian: ~39.42 USD

Therefore, Navin earns the most, followed by Ian, then Luka.
</execution_3.2>
</Execution_3>

<Plan_4>
Based on execution_3.1:
Therefore, Navin earns the most. Wait, but let me check if these calculations are correct.

Wait, maybe I made a mistake in calculations. Let me verify each step again.

<prompt_4.1> Re-evaluate and verify the USD earnings calculations for Navin, Luka, and Ian. </prompt_4.1>
-----

Based on execution_3.2:
Wait, but let me check again. Maybe there's a mistake in calculation. Let me use another approach.

<prompt_4.2> Re-check the USD earnings calculations using an alternative method to confirm the result. </prompt_4.2>
</Plan_4>

<Execution_4>
<execution_4.1>
Starting with Navin: 160 rupees per hour. 8 hours: 160*8=1280 rupees. Exchange rate: 1 USD=32.35 rupees. So 1280 /32.35. Let me compute this division more accurately. Let's use calculator steps.

1280 ÷ 32.35. Let's see:

32.35 * 39 = 32.35*40 -32.35=1294 -32.35=1261.65. Wait, no. Wait, 32.35*39=32.35*(40-1)=32.35*40 -32.35=1294 -32.35=1261.65. But 1261.65 is less than 1280. So 32.35*39=1261.65. Then 1280 -1261.65=18.35. So 18.35 /32.35=0.567. So total is 39.567 USD, approximately $39.57.

For Luka: 25 kuna per hour. 8 hours: 25*8=200 kuna. Exchange rate: 1 USD=5.18 kuna. So 200 /5.18. Let's compute that. 5.18*38=196.84. 200 -196.84=3.16. 3.16 /5.18≈0.61. So total is 38.61 USD, approximately $38.61.

Ian: 34 pula per hour. 8 hours: 34*8=272 pula. Exchange rate:1 USD=6.95 pula. So 272 /6.95. 6.95*39=269.05. 272 -269.05=2.95. 2.95 /6.95≈0.424. So total is 39.424, approximately $39.42.

So Navin: ~39.57, Ian: ~39.42, Luka: ~38.61. Therefore, Navin still earns the most, followed by Ian, then Luka.
</execution_4.1>

<execution_4.2>
Convert each person's earnings to INR (Indian Rupees) first, but since the exchange rates are against different currencies, maybe better to convert each to USD.

Alternatively, compute exact values.

Navin: 160 rupees/hour *8 =1,280 rupees.

1 US dollar =32.35 Mauritius rupees. So 1 Mauritius rupee =1/32.35 USD.

Therefore, 1,280 rupees * (1 USD /32.35 rupees) =1,280 /32.35 USD.

Let me compute 1,280 ÷32.35.

Let me do this division precisely.

32.35 | 1280.00

32.35 * 39 = 1,259.65

1280.00 -1259.65=20.35

So 20.35 /32.35=0.629

So total is 39.629, which is approximately 39.63 USD.

Similarly for Luka:

200 kuna /5.18 kuna per USD=200/5.18=?

5.18*38=196.84

200-196.84=3.16

3.16/5.18≈0.6107

So total≈38.6107 USD.

Wait, earlier I had 38.54, but more accurate is 38.61.

Similarly for Ian:

272 /6.95=?

6.95*39=269.05

272-269.05=2.95

2.95/6.95≈0.424

So 39.424≈39.42 USD.

Therefore:

Navin: ~39.63

Luka: ~38.61

Ian: ~39.42

So Navin still highest, then Ian, then Luka. So the answer would be Navin.

But let me check if the exchange rates are correctly applied. For example, is the exchange rate for Mauritius rupee 1 USD =32.35 rupees, so to convert rupees to USD, divide by 32.35. Yes. Similarly for others. So the calculations seem correct.

Alternatively, maybe check by converting to another currency first, but since we need to compare USD, converting each to USD is correct.

Alternatively, compute the earnings in each currency and then compare. But since USD is the common currency, the relative values should be the same.

Alternatively, compute the effective hourly rate in USD and then multiply by 8.

For Navin: 160 rupees/hour /32.35 ≈4.95 USD/hour. Multiply by8: ~39.63.

For Luka:25 kuna/hour /5.18≈4.82 USD/hour. Multiply by8: ~38.54.

For Ian:34 pula/hour /6.95≈4.89 USD/hour. Multiply by8: ~39.12.

Wait, hold on. Wait, 34 divided by 6.95 is approximately 4.89? Let me compute that.

34 ÷6.95.

6.95*4=27.8

34-27.8=6.2

6.2 /6.95≈0.893.

So 4.893. So 4.893 *8=39.144. So approximately 39.14 USD.

So that's a bit different from previous calculation. Wait, but 272 /6.95=39.42. Hmm. Wait, which is correct?

Wait, 34 pula per hour. 8 hours: 34*8=272 pula.

272 divided by 6.95 pula per USD. So 272 /6.95=39.423 USD.

But if we compute 34 /6.95=4.89 pula per hour? Wait, no. Wait, 34 pula per hour divided by exchange rate of 6.95 pula per USD. So 34 /6.95= approximately 4.89 USD per hour. Then 4.89*8=39.12. But 272 /6.95=39.42. Which is correct?

Wait, there's a discrepancy here. Let me check 34 /6.95. Let's compute 34 divided by 6.95.

6.95 goes into 34 how many times? 6.95*4=27.8, 6.95*5=34.75 which is too much. So 4 times. 34 -27.8=6.2. Bring down a zero: 62.0.

6.95 goes into 62.0 about 8 times (6.95*8=55.6). 62.0 -55.6=6.4. Bring down a zero: 64.0.

6.95 goes into 64.0 about 9 times (6.95*9=62.55). 64.0 -62.55=1.45. So total is 4.89... So approximately 4.89. So 4.89*8=39.12. But 272 /6.95=39.42. Wait, why the difference?

Wait, no. Wait, 34 pula per hour. So per hour, 34 pula. 8 hours: 34*8=272 pula. Then 272 pula divided by 6.95 pula per USD is 272/6.95=39.423 USD. But if we convert 34 pula to USD per hour first: 34/6.95≈4.89 USD per hour. Then multiply by 8: 4.89*8≈39.12. Wait, but 272/6.95 is 39.423. So why the difference?

Wait, let me compute 34/6.95. Let's do this precisely.

34 divided by 6.95. Let's write 34 as 34.000.

6.95 | 34.000

6.95 goes into 34 4 times (4*6.95=27.8). Subtract 27.8 from 34: 6.2.

Bring down a 0: 62.0.

6.95 goes into 62.0 8 times (8*6.95=55.6). Subtract 55.6 from 62.0: 6.4.

Bring down a 0: 64.0.

6.95 goes into 64.0 9 times (9*6.95=62.55). Subtract 62.55 from 64.0: 1.45.

Bring down a 0: 14.5.

6.95 goes into 14.5 2 times (2*6.95=13.9). Subtract 13.9 from 14.5: 0.6.

Bring down a 0: 6.0.

6.95 goes into 6.0 0 times. So we have 4.892... So approximately 4.892 USD per hour.

Multiply by 8: 4.892*8=39.136 USD.

But 272 /6.95: Let's compute 272 divided by 6.95.

6.95 | 272.000

6.95*39=269.05. Subtract from 272.000: 272.000 -269.05=2.95.

So 2.95 /6.95=0.424. So total is 39.424. So 39.424 USD.

Wait, so which is correct? There's a discrepancy here. Because converting per hour first and then multiplying by 8 gives 39.136, but converting total pula to USD gives 39.424. Which is correct?

Wait, this is a problem of unit conversion. If you have 34 pula per hour, and the exchange rate is 6.95 pula per USD, then the rate is 34 pula/hour = (34 /6.95) USD/hour ≈4.892 USD/hour. Therefore, over 8 hours, it's 4.892*8≈39.136 USD. However, 34*8=272 pula, and 272 /6.95≈39.424 USD. These two results should be the same. So why the difference?

Wait, this suggests a miscalculation. Let me check 34*8. 34*8=272. Correct. 272 divided by 6.95. Let me compute 272 ÷6.95. Let's do this division step by step.

6.95 * 39 = 269.05. 272 -269.05=2.95. So 2.95 /6.95=0.424. So total is 39.424. So 39.424 USD.

But 34/6.95=4.892. 4.892*8=39.136. So discrepancy here. That can't be. There must be a mistake here.

Wait, no. Wait, 34 pula per hour. So per hour, 34 pula. 8 hours: 34*8=272 pula. Then 272 pula divided by 6.95 pula per USD is 272/6.95=39.424. Alternatively, converting 34 pula to USD per hour: 34/6.95≈4.892 USD per hour. Then 4.892*8≈39.136. These two should be equal. So why the difference?

Wait, unless I made a calculation error. Let me check 34/6.95 again.

34 divided by 6.95. Let's do this in another way. Multiply numerator and denominator by 100 to eliminate decimals: 3400 /695. Let's divide 3400 by 695.

695*4=2780. 3400-2780=620. Bring down a 0: 6200.

695*8=5560. 6200-5560=640. Bring down a 0: 6400.

695*9=6255. 6400-6255=145. Bring down a 0: 1450.

695*2=1390. 1450-1390=60. So now we have 4.892... So 4.892 USD per hour. Then 4.892*8=39.136. But 272/6.95=39.424. Wait, that's inconsistent. There's a problem here.

Wait, no, actually, 34*8=272. 272 divided by 6.95 is 39.424. But 34 divided by 6.95 is 4.892, multiplied by 8 is 39.136. So why the difference? There's a discrepancy here. That suggests an error in calculation. Let me verify with another approach.

Wait, 34 pula per hour. If 1 USD =6.95 pula, then 1 pula =1/6.95 USD≈0.1436 USD. So 34 pula per hour *0.1436 USD/pula≈4.886 USD per hour. Multiply by 8≈39.088 USD. Then 272 pula *0.1436≈39.088 USD. So that's the same as converting total pula. So why earlier when I converted 34/6.95, multiplied by 8, I got 39.136, but when converting pula per hour, I get 39.088? Because of rounding errors in the intermediate steps.

Ah, right. Because when I converted 34/6.95≈4.892, then multiplied by 8, I rounded 4.892 to three decimal places, leading to a slight error. If I use more precise numbers:

34 /6.95 = exactly 3400/695. Let's divide 3400 by 695.

695*4=2780. 3400-2780=620. So 3400/695=4 + 620/695.

620/695=124/139≈0.892. So 4.892.

Multiply by 8: 4.892*8=39.136. But if we compute 34 pula/hour *8=272 pula. 272/6.95=39.42372 USD. So which is correct?

Wait, this inconsistency is confusing. Let me check with exact fractions.

34 pula/hour. 8 hours: 272 pula.

272 divided by 6.95. Let's convert 6.95 to a fraction. 6.95=695/100=139/20. So 272/(139/20)=272*(20/139)=5440/139≈39.424.

Alternatively, 34/ (139/20)=34*(20/139)=680/139≈4.892. Then 4.892*8=39.136.

Wait, so why the difference? There must be a mistake here. Let me check with calculator inputs.

Wait, 34 divided by 6.95. Let me compute 34 ÷6.95.

6.95 goes into 34 approximately 4.89 times. Then 4.89*8=39.12. But 272/6.95=39.42. So which is correct?

Wait, perhaps the error is due to the exchange rate being given to three decimal places? Wait, the exchange rates are given as 1 USD=32.35 Mauritius rupees, 1 USD=5.18 kuna, and 1 USD=6.95 pula. So these are precise to the hundredth place. So perhaps in the problem, the exchange rates are considered exact, so we need to use precise division.

Let me use exact division:

Navin: 1,280 /32.35=39.63... exact value is 1280 ÷32.35=39.63 approximately.

Luka:200 /5.18=38.61... approximately.

Ian:272 ÷6.95=39.42... approximately.

So the precise values are Navin: ~39.63, Ian: ~39.42, Luka: ~38.61. So Navin still highest. Therefore, the answer is Navin.

But just to make sure, let me check if the exchange rates are correctly applied.

For Navin: 160 R Maur per hour. 8 hours: 1280 R Maur. 1 USD=32.35 R Maur. So 1280 /32.35≈39.63 USD.

Luka:25 kuna/hour. 8 hours:200 kuna. 1 USD=5.18 kuna. 200/5.18≈38.61 USD.

Ian:34 pula/hour. 8 hours:272 pula. 1 USD=6.95 pula. 272/6.95≈39.42 USD.

Yes, so Navin and Ian are close, but Navin is slightly higher. Therefore, Navin earns the most.
</execution_4.2>
</Execution_4>

<Plan_5>
Based on execution_4.2:
None
</Plan_5>

<Execution_5>
No prompt to execute.
</Execution_5>

<Final_answer>
Therefore, Navin would earn the most after working an eight-hour day, which can be expressed as $\boxed{\text{Navin}}$.
</Final_answer>
</think>