Okay, let's see. Kathy has $300 USD and wants to withdraw half in British pounds and half in euros. Then we need to find out how many more euros than pounds she'll have. The exchange rates are given: 1 pound is 1.64 USD and 1 euro is 1.32 USD. Hmm, so first, she's splitting her $300 equally into two parts: half in pounds and half in euros. That means she's withdrawing $150 into pounds and $150 into euros. Then we need to convert each amount into their respective currencies and find the difference between the two. Let me break it down step by step.

First, for the pounds. She's withdrawing $150. Since 1 pound equals 1.64 USD, to find out how many pounds that is, we divide the USD amount by the exchange rate. So, pounds = 150 / 1.64. Let me calculate that. 150 divided by 1.64. Let me do this division. 1.64 goes into 150 how many times? Let's see: 1.64 * 90 = 147.6. So 90 pounds would be 147.6 USD. Then the remaining is 150 - 147.6 = 2.4 USD. So 2.4 / 1.64 is approximately 1.463 pounds. So total pounds would be 90 + 1.463 ≈ 91.463 pounds. Let me check that again. 150 / 1.64. Let me do it more accurately. 1.64 * 91 = 1.64*90 +1.64*1 = 147.6 +1.64=149.24. Then 150 -149.24=0.76. So 0.76 /1.64=0.463. So yes, 91.463 pounds. So approximately 91.46 pounds.

Now for the euros. She's withdrawing $150. Since 1 euro is 1.32 USD, the number of euros would be 150 /1.32. Let's calculate that. 1.32 * 113 = 1.32*100 +1.32*13=132 +17.16=149.16. Then 150 -149.16=0.84. So 0.84 /1.32=0.636. So total euros is 113 +0.636≈113.636 euros. So approximately 113.64 euros.

Now, the question is how many more euros than pounds she has. So subtract pounds from euros: 113.64 -91.46≈22.18. Then round to the nearest whole number. So that's 22. But wait, let me check the calculations again to make sure.

For pounds: 150 /1.64. Let me use a calculator. 150 divided by 1.64. Let me compute 150 ÷1.64. 1.64 × 90 = 147.6. 150 -147.6 =2.4. 2.4 ÷1.64 = approximately 1.463. So 90 +1.463=91.463. So 91.463 pounds.

For euros: 150 ÷1.32. 1.32 ×113=149.16. 150 -149.16=0.84. 0.84 ÷1.32=0.636. So 113.636 euros.

Difference: 113.636 -91.463=22.173. Rounded to the nearest whole number is 22. So the answer is 22.

Wait, but let me check if the exchange rates are correctly applied. For pounds, 1 USD = 1/1.64 pounds. So 150 USD is 150 * (1/1.64) pounds. Similarly for euros, 150 USD is 150 * (1/1.32) euros. So the calculations are correct. Yes, so pounds would be 150 /1.64 and euros 150 /1.32. The difference is 150(1/1.32 -1/1.64). Let me compute that directly. 1/1.32 is approximately 0.757575, and 1/1.64 is approximately 0.609756. So the difference per dollar is 0.757575 -0.609756≈0.147819. Multiply by 150: 150*0.147819≈22.17285. So yes, 22.17285, which rounds to 22.

Alternatively, maybe I can compute the difference directly. Let's see. 150 divided by 1.32 minus 150 divided by 1.64. Let's compute both fractions:

150/1.32 = (150 * 100)/132 = 15000/132 = 15000 ÷132. Let's divide 15000 by 132. 132*113=14916. 15000-14916=84. So 84/132=0.636. So 113.636 euros.

150/1.64 = (150*100)/164=15000/164. Let's divide 15000 by 164. 164*90=14760. 15000-14760=240. 240/164=1.463. So 91.463 pounds.

Difference: 113.636 -91.463=22.173. Rounded to 22. So yes, same result. Therefore, the answer is 22 euros more than pounds.

I think that's correct. Let me just verify once again. If she withdraws $150 into pounds at 1.64, she gets 150/1.64≈91.46. Into euros at 1.32, she gets 150/1.32≈113.64. The difference is 113.64 -91.46≈22.18, which rounds to 22. Yes, that seems right.
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