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Chapter 2: Problem 76

Solve each problem. (Round answers to the nearest tenth as necessary.) If 8 U.S. dollars can be exchanged for 150.775 Mexican pesos, how many pesos can be obtained for \(\$ 65 ?\) (Round to the nearest tenth.)

Short Answer

Expert verified
1,224.0 pesos

Step by step solution

01

- Identify the Exchange Rate

The problem gives the exchange rate as 8 U.S. dollars = 150.775 Mexican pesos.
02

- Calculate the Exchange Rate per Dollar

Divide the amount of pesos by the amount of dollars to find the rate per dollar: \[ \frac{150.775 \text{ pesos}}{8 \text{ dollars}} = 18.846875 \text{ pesos/dollar} \]
03

- Multiply to Find Pesos for 65 Dollars

Multiply the exchange rate per dollar by 65 dollars to find how many pesos can be obtained: \[ 65 \text{ dollars} \times 18.846875 \text{ pesos/dollar} = 1,224.046875 \text{ pesos} \]
04

- Round to the Nearest Tenth

Round 1,224.046875 pesos to the nearest tenth: \[ 1,224.0 \text{ pesos} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Currency Conversion
Currency conversion is the process of transferring value from one currency to another based on the current exchange rate. In this problem, we need to convert U.S. dollars to Mexican pesos. Start by understanding the given exchange rate: 8 U.S. dollars equal 150.775 Mexican pesos. This tells us how much one currency is worth in the terms of another. To do any currency conversion, you need to know the exchange rate, which is usually provided. Once you have the exchange rate, the next step is to use it to convert the amount you want. It's essential to be careful with the calculations to ensure accuracy.
Division
Division helps us find out how much one unit of a certain quantity is worth. In this exercise, we divide to find the exchange rate per U.S. dollar. Here's how it's done: We have 8 U.S. dollars equal to 150.775 Mexican pesos. To find out how many pesos we get for one dollar, we divide 150.775 by 8. This calculation can be written as \: \[ \frac{150.775}{8} \approx 18.846875 \]. This result, 18.846875, tells us the value of one U.S. dollar in Mexican pesos. Division can be tricky, so use a calculator if needed to ensure accuracy.
Multiplication
Multiplication allows us to find the total amount of pesos for any given amount of dollars. After knowing that one U.S. dollar is approximately 18.846875 pesos, we can find out how many pesos we get for \$65. To do this, multiply 65 dollars by the exchange rate 18.846875 pesos per dollar: \[ 65 \times 18.846875 = 1,224.046875 \] pesos. Multiplication is useful in currency conversion when you want to find out the equivalent amount of one currency for a given amount of another. Always double-check your work to avoid mistakes.
Rounding Numbers
Rounding numbers makes the results easier to read and understand. After calculating 1,224.046875 pesos, we need to round to the nearest tenth as required by the problem. Look at the hundredths place (the second digit after the decimal). If it's 5 or more, we round up. If it's less than 5, we round down. In this case, 1,224.046875 becomes 1,224.0. Rounding is used in everyday math to simplify numbers and make them more manageable, especially in currency calculations where many decimal places might confuse the reader.

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