Problem 32 - Elementary Algebra

Question

The regular price of a gallon of orange juice is \(\$ 3.89\). On sale, the juice is \(\$ 3.59\) per gallon. A daycare center uses 45 gallons of milk and 32 gallons of orange juice per week. Find the amount the daycare center will save per week when the orange juice is on sale.

Step-by-Step Solution

Answer

The daycare center will save \$9.60 per week.

Step 1: Calculate Weekly Savings Per Gallon

Subtract the sale price from the regular price to find the savings per gallon. Regular price: \( \$3.89 \) Sale price: \( \$3.59 \) Savings per gallon: \( \$3.89 - \$3.59 = \$0.30 \)

Step 2: Determine Total Gallons of Orange Juice Used

Identify the number of gallons of orange juice the daycare center uses per week, which is given as 32 gallons.

Step 3: Calculate Total Weekly Savings

Multiply the savings per gallon by the total number of gallons used to find the total savings per week. \Savings per gallon: \( \$0.30 \) Total gallons used: \( 32 \) Total weekly savings: \( 32 \times \$0.30 = \$9.60 \)

Key Concepts

Understanding Price Difference

To determine how much you save during a sale, you need to understand the concept of price difference. Price difference is simply the amount you save when the price of an item is reduced.
The price difference can be found by subtracting the sale price from the original price. For example, if a gallon of orange juice is regularly priced at \(\text{\textdollar}3.89\) and goes on sale for \(\text{\textdollar}3.59\), the difference is \(\text{\textdollar}3.89 - \text{\textdollar}3.59 = \text{\textdollar}0.30\). When you're aware of the price difference, you can calculate your total savings if you know how many items you want to buy.
This exercise demonstrates a practical use of price difference by calculating how much the daycare saves on orange juice when it goes on sale.

The Importance of Multiplication in Calculations

Multiplication is a fundamental skill in mathematics that allows you to calculate the total from individual amounts. In this problem, you need to use multiplication to find the total savings.
Once you know how much you save per gallon of orange juice, you multiply that amount by the number of gallons the daycare center uses each week. Let's break it down: \(\text{\textdollar}0.30\) savings per gallon \(\times\) 32 gallons of orange juice = \ \text{\textdollar}9.60 \ in total weekly savings.
Understanding how to multiply these values is crucial in a variety of real-life situations. Multiplication allows you to find totals quickly and accurately, whether you're budgeting, shopping, or planning.

Real-Life Applications of Algebra

Algebra isn't just a subject you learn in school; it has many real-life applications. This problem is a excellent example of how algebra helps you make better financial decisions.
Whenever you're dealing with quantities and prices, such as in grocery shopping or budgeting, algebra can help you figure out total costs and savings. By understanding how to calculate price differences and use multiplication, you can better manage your finances and find the best deals.
Algebra also helps you understand relationships between different values. For example, knowing how the price per gallon affects your total savings can help you make informed choices.

• Budgeting for groceries
• Calculating price discounts
• Managing expenses

So, algebra is not just confined to your math class; it's a useful tool that you can use every day to make life a bit easier and more efficient.