Currency Exchange

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Answer Key & Explanations

Currency Exchange · Grade 8 · Worksheet 1

1. Emma is traveling from Canada to the United Kingdom and needs to exchange her Canadian dollars (CAD) for British pounds (GBP). The exchange rate is 1 CAD = 0.58 GBP. The currency exchange service first applies a 2% transaction fee on the initial CAD amount, then converts the remaining money. If Emma exchanges 800 CAD, how many British pounds will she receive? Answer: 454.72 Solution: Calculate the transaction fee amount. 2% of 800 CAD = 0.02 × 800 = 16 CAD. Subtract the fee from the initial amount.
   Full step-by-step solution

   Step 1: Calculate the transaction fee amount. 2% of 800 CAD = 0.02 × 800 = 16 CAD. Step 2: Subtract the fee from the initial amount. 800 CAD - 16 CAD = 784 CAD remaining for exchange. Step 3: Convert the remaining CAD to GBP using the exchange rate. 784 CAD × 0.58 GBP/CAD = 454.72 GBP. The answer is 454.72.

2. 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

3. Emma is exchanging 450 US dollars for Canadian dollars. The exchange rate is 1 US dollar = 1.35 Canadian dollars. How many Canadian dollars will she receive? Answer: 607.50 Solution: Identify the given information. Emma has 450 US dollars. The exchange rate is 1 US dollar = 1.35 Canadian dollars.
   Full step-by-step solution

   Step 1: Identify the given information. Emma has 450 US dollars. The exchange rate is 1 US dollar = 1.35 Canadian dollars. Step 2: To convert US dollars to Canadian dollars, multiply the number of US dollars by the exchange rate. Step 3: Calculate: 450 × 1.35 = 607.50 Step 4: Emma will receive 607.50 Canadian dollars. The answer is 607.50.

4. (4.8 × 10⁷) ÷ (1.2 × 10⁴) = ? Answer: 4000 Solution: Separate the coefficients and powers of 10: (4.8 ÷ 1.2) × (10⁷ ÷ 10⁴) Divide the coefficients: 4.8 ÷ 1.2 = 4 Apply the exponent rule for division: 10⁷ ÷ 10⁴ = 10^(7-4) = 10³ Multiply the results: 4 × 10³ = 4 × 1000 = 4000 The answer is 4000.
   Full step-by-step solution

   Step 1: Separate the coefficients and powers of 10: (4.8 ÷ 1.2) × (10⁷ ÷ 10⁴) Step 2: Divide the coefficients: 4.8 ÷ 1.2 = 4 Step 3: Apply the exponent rule for division: 10⁷ ÷ 10⁴ = 10^(7-4) = 10³ Step 4: Multiply the results: 4 × 10³ = 4 × 1000 = 4000 The answer is 4000.

5. Mason is exchanging 920 US dollars to Canadian dollars. The exchange rate is 1 US dollar = 1.35 Canadian dollars. How many Canadian dollars will Mason receive? Answer: 1242 Solution: Identify the exchange rate: 1 US dollar = 1.35 Canadian dollars. Multiply the amount in US dollars by the exchange rate: 920 × 1.35. Calculate: 920 × 1.35 = 920 × (1 + 0.35) = 920 + 322 = 1242.
   Full step-by-step solution

   Step 1: Identify the exchange rate: 1 US dollar = 1.35 Canadian dollars. Step 2: Multiply the amount in US dollars by the exchange rate: 920 × 1.35. Step 3: Calculate: 920 × 1.35 = 920 × (1 + 0.35) = 920 + 322 = 1242. The answer is 1242 Canadian dollars.

6. Emma is planning a trip to Europe and needs to exchange her US dollars for euros. She has $800 USD to exchange. The current exchange rate is 1 USD = 0.85 EUR. The currency exchange service charges a 2.5% commission fee on the total amount of euros she would receive. How many euros will Emma have after the commission fee is deducted? Answer: 663 Solution: Calculate how many euros Emma would receive before the fee 800 USD × 0.85 EUR/USD = 680 EUR Calculate the 2.5% commission fee 2.5% of 680 EUR = 0.025 × 680 = 17 EUR 680 EUR - 17 EUR = 663 EUR Emma will have 663 euros after the commission fee is deducted.
   Full step-by-step solution

   Step 1: Calculate how many euros Emma would receive before the fee 800 USD × 0.85 EUR/USD = 680 EUR Step 2: Calculate the 2.5% commission fee 2.5% of 680 EUR = 0.025 × 680 = 17 EUR Step 3: Subtract the commission fee from the total euros 680 EUR - 17 EUR = 663 EUR Emma will have 663 euros after the commission fee is deducted.

7. Liam is traveling from the United States to Japan and needs to exchange his money. The exchange rate is 110 Japanese yen (JPY) for 1 US dollar (USD). Liam exchanges $250 USD and the currency exchange service charges a 3% fee on the total amount exchanged. How many Japanese yen will Liam receive after the fee is deducted? Answer: 26675 Solution: Exchange rate: 110 JPY for 1 USD Liam exchanges $250 USD. Initial yen = 250 × 110 250 × 110 = 27,500 JPY The fee is 3% of the total amount exchanged.
   Full step-by-step solution

   Let's go step-by-step. **Step 1: Calculate the initial yen amount before fees** Exchange rate: 110 JPY for 1 USD Liam exchanges $250 USD. Initial yen = 250 × 110 250 × 110 = 27,500 JPY **Step 2: Understand the fee** The fee is 3% of the total amount exchanged. "Total amount exchanged" here means the initial yen amount before fees. So fee = 3% of 27,500 JPY **Step 3: Calculate the fee in JPY** 3% of 27,500 = (3/100) × 27,500 = 0.03 × 27,500 = 825 JPY **Step 4: Subtract the fee** Yen received after fee = 27,500 − 825 = 26,675 JPY **Final Answer:** 26675

8. 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.