Simplifying the Expression

Oct 13, 2025 by miodeya.com 99 views

**Mitchell's Currency Exchange Conundrum: A Mathematical Exploration**

Understanding the Problem

Mitchell travels from the US to Canada, where he exchanges 150 US dollars for Canadian dollars. He then spends 20 Canadian dollars, returns to the US, and exchanges the remaining money back to US dollars. The question is, how many US dollars does Mitchell have left?

Step 1: Exchanging US Dollars to Canadian Dollars

When Mitchell exchanges 150 US dollars for Canadian dollars, he receives a certain amount of Canadian dollars. Let's assume the exchange rate is 1 USD = x CAD. Then, the number of Canadian dollars Mitchell receives is 150x.

Step 2: Spending Canadian Dollars

Mitchell then spends 20 Canadian dollars, leaving him with (150x - 20) Canadian dollars.

Step 3: Returning to the US and Exchanging Canadian Dollars to US Dollars

When Mitchell returns to the US, he exchanges the remaining Canadian dollars back to US dollars. Let's assume the exchange rate is 1 CAD = y USD. Then, the number of US dollars Mitchell receives is (150x - 20)y.

The Question: How Many US Dollars Does Mitchell Have Left?

To find the answer, we need to simplify the expression (150x - 20)y. Since x and y are the exchange rates, they are constants. Let's assume x = 1.3 (1 USD = 1.3 CAD) and y = 0.77 (1 CAD = 0.77 USD).

Simplifying the Expression

Substituting the values of x and y, we get:

(150x - 20)y = (150(1.3) - 20)(0.77) = (195 - 20)(0.77) = 175(0.77) = 134.75

Conclusion

Mitchell has 134.75 US dollars left.

Q&A

Q: What is the exchange rate used in this problem? A: The exchange rate used is 1 USD = 1.3 CAD and 1 CAD = 0.77 USD.

Q: How many US dollars does Mitchell have left? A: Mitchell has 134.75 US dollars left.

Q: What happens if Mitchell spends more Canadian dollars? A: If Mitchell spends more Canadian dollars, he will have fewer US dollars left after exchanging the remaining Canadian dollars back to US dollars.

Q: Can we use any exchange rate in this problem? A: No, we need to use the actual exchange rates to get the correct answer.

Q: Is this problem relevant to real-life scenarios? A: Yes, this problem is relevant to real-life scenarios where people travel abroad and exchange currencies.

Q: Can we simplify the expression further? A: Yes, we can simplify the expression further by canceling out the common factors.

Q: What is the significance of the exchange rates in this problem? A: The exchange rates are crucial in determining the final amount of US dollars Mitchell has left.

Q: Can we use different exchange rates for the two transactions? A: No, we need to use the same exchange rates for both transactions to get the correct answer.

Q: Is this problem a good example of a mathematical problem? A: Yes, this problem is a good example of a mathematical problem that involves real-life scenarios and requires the application of mathematical concepts.

Q: Can we use this problem to teach mathematical concepts? A: Yes, this problem can be used to teach mathematical concepts such as exchange rates, currency conversion, and simplifying expressions.

Q: Is this problem relevant to economics? A: Yes, this problem is relevant to economics as it involves the exchange of currencies and the conversion of money.

Q: Can we use this problem to teach economics concepts? A: Yes, this problem can be used to teach economics concepts such as exchange rates, currency conversion, and the impact of exchange rates on trade.