Problem 43 - Algebra 1: Concepts and Skills

Question

In Exercises 42 and \(43,\) use 9.242 pesos per dollar as the rate of currency exchange. You are visiting Mexico and have taken \(\$ 325\) United States dollars to spend on your trip. Round to the nearest whole number. You have 840 pesos left after your trip. How many dollars will you get back?

Step-by-Step Solution

Answer

After converting the remaining pesos into dollars and rounding off to the nearest whole number, approximately 91 dollars will be received back.

Step 1: Identify the Exchange Rate

The provided exchange rate is 9.242 pesos per dollar. This rate will be used to exchange the leftover pesos into dollars.

Step 2: Calculate the Amount in Dollars

To calculate how many dollars will be received back, the remaining pesos (840) should be divided by the exchange rate (9.242). This implies using the formula: dollars = pesos / exchange rate.

Step 3: Perform the Division

Applying the formula from step 2, it's computed that: dollars = 840 / 9.242.

Step 4: Round to the Nearest Whole Number

Given that the exercise instructs to round to the nearest whole number, the result of the division made in step 3 is rounded off. This is because usually, money isn't given or received in fractions in everyday transactions.

Key Concepts

Algebraic Word Problems

Algebraic word problems require us to apply mathematical concepts and techniques to real-world scenarios. Currency exchange is a common topic for algebraic word problems because it involves direct application of division and multiplication, and understanding rates and conversions. The key is to convert the problem from words into an algebraic expression that can be solved.

In our case, the problem describes a situation where someone has pesos left after a trip to Mexico and wants to know how many dollars that represents. Expressing this problem algebraically involves identifying the 'unknown' (the amount in dollars) and using the given exchange rate as our 'constant'. The formula derived is straightforward: divide the amount of leftover pesos by the exchange rate to find the dollar amount. This simple translation from a word problem to an algebraic expression is an essential skill for solving such exercises.

Currency Conversion

Currency conversion is all about exchange rates, which tell us the value of one currency relative to another. The exchange rate is a critical part of any currency conversion problem. To convert currency, we multiply or divide by this exchange rate, depending on whether we're buying (converting to another currency) or selling (converting back to our original currency).

In the exercise, the exchange rate is given as 9.242 pesos per dollar. This means to find out the equivalent in U.S. dollars for a given amount in pesos, we divide the pesos by the exchange rate. The algebraic expression for our specific problem is therefore written as: \(\text{dollars} = \frac{\text{pesos}}{\text{exchange rate}}\), which succinctly captures the essence of currency conversion in this context.

Rounding Numbers

Rounding numbers is a mathematical process used to reduce the digits in a number while keeping its value close to what it was. The purpose of rounding can vary - it might be to simplify the numbers for easier comprehension, or, as in the case with money, because transactions don't usually include fractions of a unit.

The general rule for rounding is to look at the digit to the right of the desired decimal place or value. If this digit is five or higher, we round up. If it is four or lower, we round down. In our algebraic word problem, once the division is performed, the amount of dollars, likely a decimal, has to be rounded to the nearest whole number to represent actual currency the traveler can receive back. This demonstrates the practical application of rounding numbers in everyday situations.