Problem 332 - Prealgebra

Question

In the following exercises, solve. Recipe Andrea is making potato salad for a buffet luncheon. The recipe says the number of servings of potato salad will be twice the number of pounds of potatoes. If she buys 30 pounds of potatoes, how many servings of potato salad will there be?

Step-by-Step Solution

Answer

There will be 60 servings of potato salad.

Step 1: Understand the problem

The problem states that the number of servings of potato salad is twice the number of pounds of potatoes used. Andrea is buying 30 pounds of potatoes.

Step 2: Identify the formula

The formula given in the problem is: Number of servings = 2 × Number of pounds of potatoes.

Step 3: Substitute the given value into the formula

Substitute 30 for the number of pounds of potatoes in the formula: Number of servings = 2 × 30.

Step 4: Perform the multiplication

Multiply 2 by 30 to find the number of servings: Number of servings = 60.

Key Concepts

Basic Multiplication

Multiplication is a fundamental mathematical operation. It involves combining equal groups of objects to find the total number of objects. In our problem, we need to multiply the number of pounds of potatoes by 2 to find the number of servings.

If you think about it, multiplication is repeated addition. For example, 2 times 30 is the same as adding 30 twice: 30 + 30 = 60. This concept is helpful because it makes the multiplication process easier to understand.

In real-life problems like making potato salad, we often use multiplication to scale up recipes or quantities. If a recipe serves one person and we want to serve two people, we multiply the recipe by 2.

Understanding this will help you solve similar problems with ease.

Understanding Formulas

Formulas are like instructions that help us solve problems. They usually involve mathematical operations and variables. In our exercise, the formula is provided to calculate the number of servings:

\( \text{Number of servings} = 2 \times \text{Number of pounds of potatoes} \)

The formula ensures that we apply the correct operations to get the desired result. It’s important to identify and understand the formula given in any problem, as it tells us how to proceed.

By substituting the value from the problem (30 pounds of potatoes), we can use the formula to find the solution:
\( \text{Number of servings} = 2 \times 30 \)

Which simplifies to 60 servings.

Learn to recognize the parts of a formula:

• The constants: These are fixed numbers, like the 2 in our formula.
• The variables: These are the changing numbers, like the number of pounds of potatoes.

Understanding these components allows you to apply the formula correctly.

Step-by-Step Problem Solving

Solving word problems step-by-step makes them easier to handle. Let’s break it down with our potato salad example:

1. **Understand the Problem:**
We need to find the number of servings from the pounds of potatoes.
2. **Identify the Formula:**
Use the given formula: \( \text{Number of servings} = 2 \times \text{Number of pounds of potatoes} \)
3. **Substitute Values:**
Insert the given number of pounds into the formula: \( \text{Number of servings} = 2 \times 30 \)
4. **Perform the Calculation:**
Multiply 2 by 30 to get the number of servings: \( 2 \times 30 = 60 \)
Following these steps ensures you stay organized and don’t miss any details. It also makes complex problems seem simpler by breaking them into manageable parts. Next time you encounter a word problem, remember to slow down and follow these steps carefully.