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In December \(2016,\) the price of wheat was \(\$ 4.0425\) per bushel. How much would 100 bushels of wheat cost at this price? (Source: ndwheat.com)

Short Answer

Expert verified
100 bushels cost $404.25.

Step by step solution

01

Identify the Given Information

We are given the price of one bushel of wheat, which is \( \$4.0425 \), and we need to find the total cost of 100 bushels.
02

Formulate the Calculation

To find the total cost, multiply the price of one bushel by the number of bushels: Total Cost = Price per Bushel \( \times \) Number of Bushels.
03

Substitute the Values

Substitute the given values into the formula: Total Cost = \( 4.0425 \times 100 \).
04

Perform the Multiplication

Calculate the multiplication: \( 4.0425 \times 100 = 404.25 \). This is done by simply moving the decimal two places to the right, as multiplying by 100 involves scaling the number by two place values.
05

Conclude the Solution

The cost of 100 bushels of wheat is \( \$404.25 \).

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Key Concepts

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

Cost Calculation
Cost calculation is the process of determining the total amount of money required to purchase or produce a certain quantity of goods or services. In simple terms, it's about figuring out how much something will cost in total.

In our example, we have the unit price of a single item, which is the price for one bushel of wheat, priced at \(\$4.0425\). To find out how much it will cost to buy 100 bushels, we multiply this unit price by the total quantity needed, which is 100.

This is done through a basic multiplication, which will give us the overall cost. This method is efficient and direct and can be applied in countless scenarios where you need to find out the total expenses for buying or producing multiple items. Understanding it helps in budgeting and financial planning as well.
Decimal Multiplication
Decimal multiplication involves multiplying numbers that have digits to the right of the decimal point. In mathematics, decimals are used to represent fractions of a whole number, and knowing how to multiply them is essential.

For example, multiplying \(4.0425\) by \(100\) demonstrates how to scale a decimal number. Here, the technical shortcut is to move the decimal point two places to the right, which accomplishes the same as multiplying manually.

When multiplying a decimal by a whole number like 100, each place value shifts to the left by as many zeros as the whole number has. So, in this scenario, the calculation \(4.0425 \times 100 = 404.25\) shows that the decimal has moved from its original position. Mastery of this technique simplifies computation of costs and quantities efficiently.
Unit Price Calculation
Understanding unit price calculation is crucial in economics and personal finance. A unit price is the cost associated with a single unit of measure, which helps in comparing prices and evaluating the best purchase option.

In our scenario, the unit price of wheat is \(\$4.0425\) per bushel. Knowing this unit price enabled us to easily calculate the total cost for 100 bushels. It provides a clear and straightforward way to assess expenses, especially when dealing with bulk purchases.

By always knowing how to find a unit price, you can break down complex purchases into more manageable figures, which allows for more informed and economically sound decisions. It serves as a foundation for further financial calculations and strategies.

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