Problem 113 - Prealgebra

Question

To promote her business, Theresa mails several packages via Media Mail. One package weighing 2 lbs. costs \(2.77, another package weighing 3 lbs. costs \)3.16, and the third package weighing 5 lbs. costs $3.94 to mail. What was the average cost per pound to mail the packages? Round your result to the nearest penny. www.usps.com/prices/media-mailprices.htm

Step-by-Step Solution

Answer

The average cost per pound is $0.99.

Step 1: Add the Weights

First, sum the weights of all the packages. These are 2 lbs., 3 lbs., and 5 lbs. So, the total weight is calculated as follows:\[ 2 + 3 + 5 = 10 \] lbs.

Step 2: Add the Costs

Next, sum up the costs of mailing these packages. The costs provided are \(2.77\), \(3.16\), and \(3.94\). Add them as follows:\[ 2.77 + 3.16 + 3.94 = 9.87 \] dollars.

Step 3: Calculate the Average Cost per Pound

Now, calculate the average cost per pound by dividing the total cost by the total weight. Use the formula:\[ \text{Average Cost per Pound} = \frac{\text{Total Cost}}{\text{Total Weight}} \]Substitute the values we found:\[ \frac{9.87}{10} = 0.987 \] dollars per pound.

Step 4: Round to the Nearest Penny

Finally, round the result from the previous step to the nearest penny. \(0.987\) rounded to the nearest penny is \(0.99\).

Key Concepts

Weight Calculation

When dealing with multiple items, such as packages, the first thing we need to do is find the total weight. This is called weight calculation. In our scenario, we have packages weighing 2 lbs., 3 lbs., and 5 lbs. To find the total, simply add these weights together:

• Add 2 lbs. and 3 lbs., which gives 5 lbs.
• Add the resulting 5 lbs. to the remaining 5 lbs., resulting in 10 lbs.

This method allows us to know the collective weight of items before proceeding to calculate further costs or averages.

Cost Addition

Once we know the total weight, the next step is figuring out the total cost by adding up the individual costs of each package. This is known as cost addition. We have three amounts in dollars: $2.77, $3.16, and $3.94. Here’s how you add them:

• Add $2.77 and $3.16. This equals $5.93.
• Then add the resultant $5.93 to $3.94.
• You will get a total cost of $9.87.

By doing this, you determine how much all the packages cost cumulatively to mail.

Rounding Numbers

Rounding numbers involves adjusting a number to make it simpler or more intuitive, often to a desired level of precision. In our average cost calculation, after performing division, we obtain 0.987 dollars per pound. Because currency is typically displayed to two decimal points, you need to round 0.987 to the nearest penny:

• The digit in the thousandths place is 7, which is above 5, so we round the hundredths place up.
• Thus, 0.987 becomes 0.99 when rounded to two decimal places.

Rounding helps provide more practical and understandable results in monetary calculations.

Division in Arithmetic

Division in arithmetic involves splitting a quantity into equal parts. In the context of our problem, we are dividing the total mailing cost by the total weight to find the average cost per pound. The formula for average is:

• Total Cost / Total Weight = Average Cost per Unit.

Apply this to your values: divide $9.87 by 10 lbs., which is:\[ \frac{9.87}{10} = 0.987 \]This division tells us how much each pound costs on average. Division is a fundamental operation that helps distribute a total amount uniformly.