Question
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Write an equation that gives the amount of money in pesos, \( p \), as a function of the dollar amount, \( d \), being exchanged.

Ask by Whittaker Rowe. in the United States
Feb 03,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The amount in pesos \( p \) is equal to the dollar amount \( d \) multiplied by the exchange rate \( r \). So, \( p = d \times r \).

Solution

To express the amount of money in pesos (\( p \)) as a function of the dollar amount (\( d \)) being exchanged, you can use the following equation: \[ p = d \times r \] **Where:** - \( p \) is the amount in pesos. - \( d \) is the amount in dollars. - \( r \) is the exchange rate (pesos per dollar). **Example:** If the exchange rate is \( 20 \) pesos per dollar (\( r = 20 \)), and you exchange \( 50 \) dollars (\( d = 50 \)), the amount in pesos would be: \[ p = 50 \times 20 = 1000 \text{ pesos} \] **Function Notation:** Alternatively, you can express this relationship using function notation: \[ p(d) = d \times r \] This clearly shows that \( p \) is a function of \( d \) with \( r \) as the constant exchange rate.

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Bonus Knowledge

To find the amount of money in pesos \( p \) as a function of the dollar amount \( d \), we can use the current exchange rate between dollars and pesos. Suppose the exchange rate is \( r \) pesos per dollar. The equation would be: \[ p = r \cdot d \] This equation means that for every dollar exchanged, you multiply by the exchange rate to get the corresponding amount in pesos. Now, if we consider the factors affecting exchange rates, it’s fascinating to see how geopolitical events or economic indicators can fluctuate them. For example, a country's inflation rate or interest rates can significantly raise or lower its currency value compared to others! When exchanging currency, always check the latest exchange rates and be aware of additional fees charged by banks or exchange services. A common mistake is assuming that the displayed rates are the final amounts you will actually receive, as commissions can eat into your expectations!

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