Question

Apples cost \(\$ 0.79\) per pound. What conversion factor could be used to determine how many pounds of apples could be bought for \(\$ 2.00 ?\)

Short answer

For \(\$2.00\), you can buy approximately 2.54 pounds of apples using a conversion factor of \(\frac{1}{0.79} \approx 1.27\) pounds of apples per dollar.

Step-by-step solution

Identify the given information

We are given the cost per pound of apples, which is \(0.79. We also have a target amount of money to spend, which is \)2.00.

Calculate the inverse of the cost per pound

Since we want to find how many pounds of apples can be bought for $2.00, we need to find the inverse of the cost per pound. To find the inverse, divide 1 by the given cost per pound, such that; Conversion factor = \(\frac{1}{0.79}\)

Calculate the conversion factor

Now, we will find the inverse value. Conversion factor = \(\frac{1}{0.79} \approx 1.27\) This conversion factor (1.27) represents the number of pounds of apples that can be bought for $1.00.

Use the conversion factor to find the number of pounds for $2.00

We can now use the conversion factor to determine how many pounds of apples can be bought for $2.00. Pounds of apples = Conversion factor × Amount of money Pounds of apples = \(1.27 × 2\)

Calculate the final answer

Multiplying the conversion factor by the amount of money, we get; Pounds of apples = \(1.27 × 2 = 2.54\) So, 2.54 pounds of apples can be bought for $2.00.

Key concepts

Conversion Factor

In the world of unit conversion, a conversion factor is a numerical value used to change one set of units to another, while keeping the amount the same. For example, if you have a price per unit like dollars per pound, the conversion factor will help you switch between the two.
If you're wondering why this matters, imagine needing to understand how many pounds one can buy with a specific amount of money — that's when knowing the conversion factor becomes super helpful!
To determine the conversion factor for apples in our example, where apples cost $0.79 per pound, you would calculate how many pounds can be bought per unit of currency (in this case, $1). This requires calculating the inverse of the cost per pound, which gives us a handy numerical tool to switch from dollars to pounds whenever you need it.

Cost Calculation

When calculating costs, especially with conversions, understanding how to handle the given figures is essential. If you want to find out how much of a product you can buy with a particular budget or how much that product will cost, cost calculation is your go-to method.
Let's consider the example where we know the conversion factor is 1.27 pounds per $1.00. Now, to determine how much apples one can buy for $2.00, simply multiply the conversion factor by the target amount.

• Conversion factor for apples = 1.27 pounds/$1.00
• Amount of money = $2.00
• So, pounds of apples = 1.27 × 2 = 2.54 pounds

This illustrates the importance of clear cost calculation: with just a few steps, you can translate your budget into physical quantities — no more guesswork!

Inverse Calculation

Inverse calculation is a neat mathematical trick that helps reverse a given relationship. Much like flipping things upside down, it is used to derive one outcome from another in unit conversion problems.
In this case, we started with the cost per pound (\(0.79 per pound) and needed to figure out how many pounds that cost could buy with a dollar. The inverse operation helps by changing a cost per unit into units per cost. We achieve this by doing one divided by the cost per unit:

• Inverse Calculation: \)\frac{1}{0.79}\ ≈ 1.27i.e., 1.27 pounds per $1.00

This inverse ratio allows a seamless transition between cost and quantity, providing a foundation to solve similar real-world financial queries. It's a handy tool to keep in mind whenever you're dealing with cost conversions.