Currency Exchange

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Answer Key & Explanations

Currency Exchange · Grade 8 · Worksheet 1

1. Liam is traveling from the United States to Japan and needs to exchange his US dollars for Japanese yen. The exchange rate is 1 USD = 110 JPY. If Liam exchanges $250 and the currency exchange service charges a 3% fee on the total amount exchanged, how many Japanese yen will Liam receive? Answer: 26675 Solution: The exchange rate is 1 USD = 110 JPY. Liam exchanges $250. Base JPY = 250 × 110 Base JPY = 27500 JPY The exchange service charges a 3% fee on the total amount exchanged in USD.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Calculate the base amount in JPY before fees** The exchange rate is 1 USD = 110 JPY. Liam exchanges $250. Base JPY = 250 × 110 Base JPY = 27500 JPY --- **Step 2: Understand the fee** The exchange service charges a 3% fee on the **total amount exchanged** in USD. That means the fee is 3% of $250. Fee in USD = 3% of 250 Fee in USD = (3/100) × 250 Fee in USD = 0.03 × 250 Fee in USD = 7.50 --- **Step 3: Subtract the fee from the dollars exchanged** Amount in USD after fee = 250 − 7.50 Amount in USD after fee = 242.50 --- **Step 4: Convert this net USD amount to JPY** Net JPY = 242.50 × 110 First: 242 × 110 = 242 × 100 + 242 × 10 = 24200 + 2420 = 26620 Then: 0.50 × 110 = 55 So total = 26620 + 55 = 26675 --- **Step 5: Final answer** Liam receives **26675 JPY**. --- **Check alternative method** (to verify): Another way: Fee is 3% of $250, so Liam effectively gets 97% of $250 converted to JPY. 0.97 × 250 = 242.50 USD (same as before) 242.50 × 110 = 26675 JPY. --- **Answer:** 26675

2. Liam is traveling to Japan and needs to exchange his U.S. dollars for Japanese yen. The exchange rate is 110 yen per U.S. dollar. The currency exchange service charges a flat fee of $5 for the transaction. If Liam exchanges $200, how many Japanese yen will he receive after the fee is deducted? Answer: 21450 Solution: The exchange rate is 110 yen per 1 U.S. dollar.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Understand the exchange rate** The exchange rate is 110 yen per 1 U.S. dollar. This means: 1 USD = 110 JPY --- **Step 2: Calculate the yen for $200 before fees** Liam exchanges $200, so: Yen before fees = 200 × 110 Yen before fees = 22000 JPY --- **Step 3: Account for the flat fee** The service charges a flat fee of $5. This fee is taken from the $200 before conversion, so the amount actually converted is: Amount converted = 200 − 5 = 195 USD --- **Step 4: Convert the reduced amount to yen** Yen received = 195 × 110 195 × 100 = 19500 195 × 10 = 1950 Add them: 19500 + 1950 = 21450 JPY --- **Step 5: Final answer** After the $5 fee is deducted, Liam receives **21450 yen**. --- **Answer:** 21450

3. Liam is traveling to Japan and needs to exchange his money. He has $350 USD to convert to Japanese Yen. The exchange rate is 1 USD = 110 JPY, but the currency exchange service charges a 3% fee on the total transaction. After the fee is deducted, how many Japanese Yen will Liam receive? Answer: 37345 Solution: Exchange rate: 1 USD = 110 JPY Liam has $350 USD. 350 × 110 = 38,500 JPY The fee is 3% of the total transaction. The "total transaction" here means the total USD amount being exchanged.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Calculate the initial Yen without fees** Exchange rate: 1 USD = 110 JPY Liam has $350 USD. Without fees: 350 × 110 = 38,500 JPY --- **Step 2: Understand the fee** The fee is 3% of the **total transaction**. The "total transaction" here means the total USD amount being exchanged. So the fee in USD is: 3% of 350 = (3/100) × 350 = 0.03 × 350 = 10.50 USD --- **Step 3: Subtract the fee from the USD** Amount left for exchange after fee: 350 − 10.50 = 339.50 USD --- **Step 4: Convert remaining USD to JPY** 339.50 USD × 110 JPY/USD = First: 339 × 110 = 37,290 Then: 0.50 × 110 = 55 Total: 37,290 + 55 = 37,345 JPY --- **Step 5: Final check** We can verify by another method: Total JPY before fee = 38,500 If fee was taken from JPY (3% of 38,500) = 1,155 JPY Then: 38,500 − 1,155 = 37,345 JPY Same result. --- **Final Answer:** 37345

4. Jordan is an online shopper in Mexico who wants to buy a jacket priced at 67 US dollars from a US website. The exchange rate is 21 Mexican pesos for every 1 US dollar. How many pesos does Jordan need to pay for the jacket? Answer: 1407 Solution: The exchange rate is 1 USD = 21 pesos. Multiply the price in USD by the rate: 67 × 21 = 1407 pesos.
   Full step-by-step solution

   Step 1: The exchange rate is 1 USD = 21 pesos. Step 2: Multiply the price in USD by the rate: 67 × 21 = 1407 pesos. The answer is 1407 pesos.

5. Aroha is exchanging 620 New Zealand dollars (NZD) to US dollars (USD). The exchange rate is 1 NZD = 0.60 USD. How many US dollars will Aroha receive? Answer: 372 Solution: Identify the given information. Aroha has 620 NZD. The exchange rate is 1 NZD = 0.60 USD.
   Full step-by-step solution

   Step 1: Identify the given information. Aroha has 620 NZD. The exchange rate is 1 NZD = 0.60 USD. Step 2: To convert NZD to USD, multiply the amount in NZD by the exchange rate (USD per NZD). Step 3: Calculate: 620 × 0.60 = 372. Step 4: So, Aroha will receive 372 USD. The answer is 372.

6. Harper is traveling from the United States to Japan. Harper has 933 US dollars and wants to convert them to Japanese yen. The exchange rate is 104 yen for every 1 US dollar. How many yen will Harper receive? Answer: 97032 Solution: Identify the exchange rate: 1 USD = 104 yen. Multiply the amount in USD by the rate: 933 × 104 = 97032 yen.
   Full step-by-step solution

   Step 1: Identify the exchange rate: 1 USD = 104 yen. Step 2: Multiply the amount in USD by the rate: 933 × 104 = 97032 yen. The answer is 97032 yen.

7. Mason is exchanging 372 US dollars for Canadian dollars. The exchange rate is 1 US dollar = 1.27 Canadian dollars. How many Canadian dollars will Mason receive? Answer: 472.44 Solution: Identify the given information. Mason has 372 US dollars. The exchange rate is 1 US dollar = 1.27 Canadian dollars.
   Full step-by-step solution

   Step 1: Identify the given information. Mason has 372 US dollars. The exchange rate is 1 US dollar = 1.27 Canadian dollars. Step 2: To convert US dollars to Canadian dollars, multiply the amount in US dollars by the exchange rate. Step 3: Calculate: 372 × 1.27 Step 4: First multiply 372 × 1 = 372 Step 5: Then multiply 372 × 0.27 = 372 × 27/100 = 10044/100 = 100.44 Step 6: Add the results: 372 + 100.44 = 472.44 Step 7: Mason will receive 472.44 Canadian dollars. The answer is 472.44.

8. A right triangle is drawn on a coordinate plane with vertices at (0,0), (6,0), and (6,8). A second triangle is created by reflecting the original triangle across the y-axis. What is the total area of both triangles combined? Answer: 48 Solution: Find the area of the original triangle. The vertices are (0,0), (6,0), and (6,8). This is a right triangle with legs along the x-axis and a vertical line.
   Full step-by-step solution

   Step 1: Find the area of the original triangle. The vertices are (0,0), (6,0), and (6,8). This is a right triangle with legs along the x-axis and a vertical line. The horizontal leg length is from (0,0) to (6,0), which is 6 units. The vertical leg length is from (6,0) to (6,8), which is 8 units. Area of a right triangle = (1/2) * base * height. Area = (1/2) * 6 * 8 = (1/2) * 48 = 24. Step 2: Understand the reflection across the y-axis. Reflecting across the y-axis changes the sign of the x-coordinate of each point. Original vertices: (0,0), (6,0), (6,8). After reflection: (0,0) → (0,0) (6,0) → (-6,0) (6,8) → (-6,8) Step 3: Find the area of the reflected triangle. The reflected triangle has vertices at (0,0), (-6,0), (-6,8). This is also a right triangle with legs along the x-axis (from (-6,0) to (0,0), length 6) and a vertical line (from (-6,0) to (-6,8), length 8). Area = (1/2) * 6 * 8 = 24. Step 4: Combine the areas. Total area = area of original triangle + area of reflected triangle Total area = 24 + 24 = 48. Final answer: 48