Problem 65 - Elementary and Intermediate Algebra

Question

Yusuf's cell-phone bill for July was \(\$ 82 .\) He sent a check for \(\$ 50\) and then ran up \(\$ 63\) in charges for August. What was his new balance?

Step-by-Step Solution

Answer

\$95

Step 1: Determine Yusuf's payment for July

Yusuf's original cell-phone bill for July was \(\$82\). He sent a payment (check) of \(\$50\). Subtract the payment from the original July bill: \[ \$82 - \$50 = \$32 \]So, he still owes \(\$32\) for July.

Step 2: Add August charges

Yusuf incurred \(\$63\) in charges for August. To find the new balance, add this to the remaining amount from July: \[ \$32 + \$63 = \$95 \]So, the new balance after including August charges is \(\$95\).

Key Concepts

Understanding Subtraction

Subtraction is a fundamental arithmetic operation where one number is taken away from another. In the context of word problems, like Yusuf's cell-phone bill, it helps us figure out what remains after making a payment or deduction. For Yusuf's bill, the exercise begins with his July bill of \$82\. When he pays \$50\, we subtract this amount from his bill: \[ \$82 - \$50 = \$32 \] This tells us that Yusuf still owes \$32\. Remembering the order of subtraction (minuend - subtrahend = difference) is crucial. Here, \$82\ is the minuend (the original amount), \$50\ is the subtrahend (the payment), and \$32\ is the difference (what he still owes).

Adding New Charges

Addition is another core arithmetic operation where we combine numbers to find out the total. After subtracting the payment from the original bill, we need to add new charges. In Yusuf's case, he incurred \$63\ in new charges for August. To find his new balance, we'll add these charges to the amount he still owes from July: \[ \$32 + \$63 = \$95 \] This tells us that after the new charges, Yusuf's balance is \$95\. Addition helps us understand how new amounts contribute to the total. So, whenever you face a problem where new amounts are added, remember the role of addition in calculating the new total.

Using Arithmetic Operations in Algebra

Algebra often combines various arithmetic operations (like addition and subtraction) to solve problems. In the exercise, we used both to determine Yusuf's new balance. Here's a breakdown of the combined operations:

• First, subtract the payment from the original bill to find the remaining balance.
• Then, add any new charges to this remaining balance.

This sequence helps to manage and update balances correctly. Remember that arithmetic operations follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This order ensures we perform calculations correctly and systematically. By understanding and applying these concepts, you can solve a variety of word problems in algebra effectively.