Problem 31 - Elementary Algebra

Question

The regular price of a gallon of milk is \(\$ 3.09\). On sale, the milk is \(\$ 2.39\) 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 milk is on sale.

Step-by-Step Solution

Answer

The daycare center will save \(31.50\) dollars per week.

Step 1: Determine the price difference

Subtract the sale price of a gallon of milk from the regular price. Regular price: \(3.09\) Sale price: \(2.39\). Price difference: \(3.09 - 2.39 = 0.70\)

Step 2: Calculate the weekly savings for 45 gallons

Multiply the price difference by the number of gallons the daycare center uses. Number of gallons: \(45\) Price difference per gallon: \(0.70\) Total savings: \(45 \times 0.70 = 31.50\)

Key Concepts

price difference calculation

Calculating the price difference is the first step in many word problems related to savings and expenditure. To find out how much you save when an item is on sale, subtract the sale price from the regular price. For example, if the regular price of a gallon of milk is \(\$3.09\) and the sale price is \(\$2.39\), the price difference per gallon is \(3.09 - 2.39 = 0.70\). This means you save \(\$0.70\) per gallon when the milk is on sale. Understanding this simple subtraction operation is pivotal in solving more complex word problems later on.

multiplication in algebra

In algebra, multiplication often helps in calculating total costs or savings over a period or quantity. Once you know the price difference, the next step is to determine the total savings. If the daycare center uses \(45\) gallons of milk per week, and the price difference is \(\$0.70\) per gallon, you multiply these two numbers to find the total savings. This results in \(45 \times 0.70 = 31.50\). Thus, the daycare center will save \(\$31.50\) per week when the milk is on sale. Breaking down the problem into smaller, manageable steps, like multiplication, makes it easier to ensure that you're arriving at the correct solution.

cost savings calculation

Cost savings calculations combine both understanding price differences and applying multiplication skills. These calculations help in budgeting and financial planning. In our example, you first calculate the price difference by subtracting the sale price from the regular price, as shown: \(3.09 - 2.39 = 0.70\). Then, you calculate the total weekly savings for the number of gallons used: \(45 \times 0.70 = 31.50\). Knowing how to perform cost savings calculations can help manage finances efficiently. It’s an essential skill not just in academics but also in real-life financial decisions.