Problem 6 - Prealgebra

Question

Suppose you work in a grocery store 4 hours on Friday and 5 hours on Saturday. You earn 6.25 dollars an hour. Find the total wages for that weekend.

Step-by-Step Solution

Answer

You earn 56.25 dollars for the weekend.

Step 1: Calculate Friday's Wages

To find out how much you earn on Friday, multiply the number of hours you work by your hourly wage. You work 4 hours on Friday and earn 6.25 dollars per hour, so: \[ ext{Friday's wages} = 4 ext{ hours} imes 6.25 ext{ dollars/hour} = 25 ext{ dollars} \]

Step 2: Calculate Saturday's Wages

To determine how much you earn on Saturday, use the same method. Multiply the number of hours worked by your hourly wage. You work 5 hours on Saturday and earn 6.25 dollars per hour, so: \[ ext{Saturday's wages} = 5 ext{ hours} imes 6.25 ext{ dollars/hour} = 31.25 ext{ dollars} \]

Step 3: Total Weekend Wages

Add together the wages from Friday and Saturday to find your total earnings for the weekend. \[ ext{Total weekend wages} = ext{Friday's wages} + ext{Saturday's wages} = 25 ext{ dollars} + 31.25 ext{ dollars} = 56.25 ext{ dollars} \]

Key Concepts

Understanding Multiplication in Real-Life Contexts

Multiplication is one of the fundamental operations in arithmetic. It helps us calculate the total amount when there are multiple equal groups. In the context of calculating wages, multiplication is used to find out how much money you make over a period when you know the hourly rate and the number of hours worked.
To put it simply, if you know how much you earn per hour and the number of hours you work, you multiply these two numbers to get your earnings. For example, if you earn \(6.25 per hour and work 4 hours, you would calculate your earnings for that time using:

• Amount per hour: \)6.25
• Number of hours worked: 4

The multiplication \[ 4 \times 6.25 = 25 \] helps us find out that the earnings for 4 hours of work is $25.

The Basics of Addition in Calculating Total Earnings

Addition is another essential arithmetic operation, and it’s used to combine values to find a sum. This comes in handy when you want to figure out your total earnings from multiple days of work, like in our weekend wage calculation.
After calculating the earnings from each day separately, you add them up to find out the total income. For example:

• Earnings from Friday: \(25
• Earnings from Saturday: \)31.25

To find the total earnings for the weekend, you perform the addition: \[ 25 + 31.25 = 56.25 \] This calculation shows that the combined earnings from both days amount to $56.25.

How to Accurately Calculate Hourly Wages

Calculating hourly wages is crucial for managing personal finances and understanding your income. This calculation involves both multiplication and addition, as we’ve seen in the previous sections.
You start by determining your earnings for each specific day. For each period of work, multiply the number of hours by the hourly pay rate. Once you have the total for each day, add all these daily totals together to find the entire earning over a set timeframe, such as a weekend or a week.
Let's break it down:

• Identify your hourly wage (e.g., $6.25 per hour)
• Multiply this wage by the number of hours worked each day
• Add these daily earnings for the full period you're calculating

This method ensures you accurately capture all earnings, aiding in better financial planning and budgeting, whether you're calculating for a weekend or a longer period.