Question

Working for the census, Nicholle interviews seven fewer households than Val, who interviews twice as many households as Kai. If Kai interviews s households, how many households does Nicholle interview? A. \(2 s-7 s\) B. \(2(s-7)\) C. \(2-7 s\) D. \(2 s-7\)

Short answer

D. \( 2s - 7 \)

Step-by-step solution

- Define variables

Let the number of households Kai interviews be denoted by the variable \( s \).

- Express Val's interviews

According to the problem, Val interviews twice as many households as Kai. Therefore, Val's number of interviews can be expressed as \( 2s \).

- Express Nicholle's interviews

Nicholle interviews seven fewer households than Val. Thus, Nicholle's number of interviews can be expressed as \( 2s - 7 \).

- Identify the correct answer from the options

From the expressions, the number of households Nicholle interviews is \( 2s - 7 \). Comparing this with the given options, we see that the correct option is D, \( 2s - 7 \).

Key concepts

Defining Variables

In algebra word problems, defining variables is a crucial first step. A variable represents an unknown quantity that we need to find. For instance, in this problem, we define the number of households Kai interviews as the variable \( s \). This helps us set up the relationships described in the problem. Remember:

• A variable can be any letter, but it should be chosen wisely to make equations easier to follow.
• Variables act as placeholders that we manipulate to find the desired value.

Defining the right variables is like setting the stage for solving the problem. It organizes the information and simplifies complex relationships into manageable equations.

Linear Equations

Linear equations are the backbone of many algebra problems. They're equations where the highest power of the variable is one. In this problem, the equation we need is derived from the information given:

• Kai's interviews: \( s \)
• Val's interviews: \( 2s \)
• Nicholle's interviews: \( 2s - 7 \)

To clarify:

• Val interviews twice as many households as Kai, giving us \( 2s \).
• Nicholle interviews seven fewer households than Val, resulting in \( 2s - 7 \).

Linear equations like these are straightforward because they form straight lines when graphed. They are also easy to solve since you typically only need basic algebra skills such as addition, subtraction, multiplication, and division.

Step-by-Step Solutions

Step-by-step solutions make challenging problems more manageable. Here is how it worked for this exercise:

• Step 1: Define variables - Let \( s \) be the number of households Kai interviews.
• Step 2: Express Val's interviews - Val interviews twice as many households as Kai, so Val's interviews can be written as \( 2s \).
• Step 3: Express Nicholle's interviews - Nicholle interviews seven fewer households than Val, giving us \( 2s - 7 \).
• Step 4: Identify the correct answer - Among the given options, \( 2s - 7 \) matches our expression perfectly, so the answer is option D.

Using a step-by-step approach ensures that you don't miss any details and helps in logically arriving at the correct answer. By breaking down the problem, it's easier to understand each part and see how it contributes to the final solution.