Currency Exchange

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Answer Key & Explanations

Currency Exchange · Grade 8 · Worksheet 3

1. Liam is traveling from the United States 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. However, the currency exchange service charges a 3% fee on the total amount of USD being exchanged. After the fee is deducted, how many Japanese yen will Liam receive? Answer: 37345 Solution: Liam has $350 USD. Exchange rate: 1 USD = 110 JPY. Fee: 3% of the total USD being exchanged.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Understand the problem** Liam has $350 USD. Exchange rate: 1 USD = 110 JPY. Fee: 3% of the total USD being exchanged. We need to find how many JPY he gets after the fee. --- **Step 2: Calculate the fee in USD** Fee = 3% of 350 USD Fee = (3/100) * 350 Fee = 0.03 * 350 Fee = 10.5 USD --- **Step 3: Calculate USD left after fee** USD after fee = 350 − 10.5 USD after fee = 339.5 USD --- **Step 4: Convert USD to JPY** Exchange rate: 1 USD = 110 JPY JPY received = 339.5 * 110 Let’s compute: 339.5 * 100 = 33,950 339.5 * 10 = 3,395 Add them: 33,950 + 3,395 = 37,345 --- **Step 5: Final answer** Liam will receive **37,345 JPY** after the fee. --- ANSWER: 37345

2. Emma is traveling from the United States to Mexico and needs to exchange her money. She has $180 USD to convert to Mexican pesos. The exchange rate is 1 USD = 20 MXN, but the currency exchange service charges a 2.5% fee on the total amount of pesos she would receive. After the fee is deducted, how many Mexican pesos will Emma receive? Answer: 3510 Solution: Calculate how many pesos Emma would receive without fees 180 USD × 20 MXN/USD = 3600 MXN 2.5% of 3600 MXN = 0.025 × 3600 = 90 MXN 3600 MXN - 90 MXN = 3510 MXN Emma will receive 3510 Mexican pesos after the fee is deducted.
   Full step-by-step solution

   Step 1: Calculate how many pesos Emma would receive without fees 180 USD × 20 MXN/USD = 3600 MXN Step 2: Calculate the fee amount 2.5% of 3600 MXN = 0.025 × 3600 = 90 MXN Step 3: Subtract the fee from the total 3600 MXN - 90 MXN = 3510 MXN Emma will receive 3510 Mexican pesos after the fee is deducted.

3. Emma is exchanging 850 US dollars to euros. The exchange rate is $1 = 0.90€. How many euros will she receive? Answer: 765 Solution: Identify the given information: Emma has $850, and the exchange rate is $1 = 0.90€. To convert dollars to euros, multiply the dollar amount by the exchange rate (euros per dollar). Calculate: 850 × 0.90 = 765.
   Full step-by-step solution

   Step 1: Identify the given information: Emma has $850, and the exchange rate is $1 = 0.90€. Step 2: To convert dollars to euros, multiply the dollar amount by the exchange rate (euros per dollar). Step 3: Calculate: 850 × 0.90 = 765. Step 4: So, Emma will receive 765 euros. The answer is 765.

4. Emma is traveling from Canada to Mexico and needs to exchange her Canadian dollars (CAD) for Mexican pesos (MXN). The exchange rate is 1 CAD = 15 MXN. The currency exchange service first charges a 2% commission on the original CAD amount, then converts the remaining money at the given rate. If Emma exchanges 400 CAD, how many Mexican pesos will she receive? Answer: 5880 Solution: Calculate the commission fee. Commission = 2% of 400 CAD = 0.02 × 400 = 8 CAD Calculate the amount remaining after the commission is deducted.
   Full step-by-step solution

   Step 1: Calculate the commission fee. Commission = 2% of 400 CAD = 0.02 × 400 = 8 CAD Step 2: Calculate the amount remaining after the commission is deducted. Amount after commission = 400 CAD - 8 CAD = 392 CAD Step 3: Convert the remaining Canadian dollars to Mexican pesos using the exchange rate. Pesos received = 392 CAD × 15 MXN/CAD = 5880 MXN Emma will receive 5880 Mexican pesos.

5. Sophia is planning a trip to Europe and needs to exchange her US dollars for euros. The exchange rate is 1 USD = 0.85 EUR. The currency exchange service charges a 2.5% fee on the total amount of euros received. If Sophia exchanges $400, how many euros will she have after the fee is deducted? Answer: 331.5 Solution: 400 USD × 0.85 EUR/USD = 340 EUR Calculate the 2.5% fee on the euros received 2.5% of 340 EUR = 0.025 × 340 = 8.5 EUR 340 EUR - 8.5 EUR = 331.5 EUR Sophia will have 331.5 euros after the fee is deducted.
   Full step-by-step solution

   Step 1: Calculate the initial euro amount before fees 400 USD × 0.85 EUR/USD = 340 EUR Step 2: Calculate the 2.5% fee on the euros received 2.5% of 340 EUR = 0.025 × 340 = 8.5 EUR Step 3: Subtract the fee from the initial euro amount 340 EUR - 8.5 EUR = 331.5 EUR Sophia will have 331.5 euros after the fee is deducted.

6. (4.5 × 10⁶) × (2 × 10⁻³) = ? Answer: 9000 Solution: Multiply the coefficients: 4.5 × 2 = 9 Add the exponents: 6 + (-3) = 3 Combine the results: 9 × 10³ Convert to standard form: 9 × 1000 = 9000 The answer is 9000.
   Full step-by-step solution

   Step 1: Multiply the coefficients: 4.5 × 2 = 9 Step 2: Add the exponents: 6 + (-3) = 3 Step 3: Combine the results: 9 × 10³ Step 4: Convert to standard form: 9 × 1000 = 9000 The answer is 9000.

7. 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 yen, but the currency exchange service charges a 3% fee on the total transaction. After paying the fee, how many yen will Liam receive? Answer: 37345 Solution: Exchange rate: 1 USD = 110 yen Liam has $350 USD. Yen without fee = 350 × 110 350 × 110 = 38500 yen So without any fee, he would get 38500 yen. The fee is 3% of the total transaction.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Find the yen before the fee** Exchange rate: 1 USD = 110 yen Liam has $350 USD. Yen without fee = 350 × 110 350 × 110 = 38500 yen So without any fee, he would get 38500 yen. --- **Step 2: Understand the fee** The fee is 3% of the total transaction. "Total transaction" here means the total yen value being exchanged. So fee = 3% of 38500 yen. Fee = (3/100) × 38500 = 3 × 385 = 1155 yen --- **Step 3: Subtract the fee** Yen after fee = 38500 − 1155 38500 − 1150 = 37350 37350 − 5 = 37345 --- **Step 4: Final answer** Liam will receive **37345 yen**.