Problem 54 - Elementary Algebra

Question

The price of a place setting of dishes is \(\$ 20.99\). A customer with \(\$ 845\) in a checking account bought eight place settings with her debit card. Find the ending balance in the account. Use a negative number to represent a debit.

Step-by-Step Solution

Answer

Ending Balance = \$ 677.08\

Step 1: Calculate the total cost of the place settings

Multiply the price of one place setting by the number of place settings purchased. Total cost = \(\text{Price per setting} \times \text{Number of settings}\)Total cost = \(\$ 20.99 \times 8\)Total cost = \$ 167.92\

Step 2: Subtract the total cost from the initial account balance

Subtract the total cost calculated in Step 1 from the initial account balance.Ending Balance = \(\text{Initial Balance} - \text{Total Cost}\)Ending Balance = \(\text{\textbackslash}\$ 845 - \text{\textbackslash}\$ 167.92\)Ending Balance = \$ 677.08\

Key Concepts

Multiplication

Multiplication is one of the basic arithmetic operations where you add a number to itself a certain number of times. For example, if you wanted to calculate how many total pencils you would have when you buy 5 boxes each containing 10 pencils, you multiply 5 by 10. This means you have 5 groups of 10 pencils, or:o[ 10 + 10 + 10 + 10 + 10 = 50In this exercise, the customer bought multiple place settings for a certain price each. Here's how it's done:

• Each place setting costs \$20.99.
• You multiply the cost per place setting by the number of place settings (8) the customer buys:

\[ \$20.99 \times 8 = \$167.92 \]Now, you know the total cost for the setting of dishes.

Subtraction

Subtraction is another fundamental arithmetic operation where you take one number away from another. It's used to find out how much is left when some quantity has been removed. For example, if you have 10 apples and you eat 3, you subtract 3 from 10 to find out how many apples are left: 10 - 3 = 7.

In our exercise, after finding the total cost of the place settings, you need to subtract this amount from the customer's initial account balance of \(\$845\). Here is how it works:

• Initial account balance: \(\text{\$845}\)
• Total cost of place settings: \(\text{\$167.92}\)

So, the equation to find the ending balance is:

\[ \$845 - \$167.92 = \$677.08\]The result, \(\$677.08\), is the new balance in the account after the purchase.

Debit and Credit

Understanding debit and credit is crucial for managing finances. A debit represents money taken out of an account, while a credit represents money added. When you use a debit card, you typically see a subtraction in your account balance, which is considered a debit.

In the exercise scenario, the customer used a debit card to purchase the place settings. So the total cost, \(\$167.92\), is a debit (a negative number):

• Initial account balance: \(\text{\$845}\)
• Debit for place settings: \(\text{\$167.92}\)
• Ending balance: \(\text{\$677.08}\)

Debit transactions reduce your balance. It's essential to track these to avoid overdraft fees and to have a clear picture of your available funds.