Question

Susan weighs \(m\) pounds more than Anna does, and together they weigh a total of \(n\) pounds. Which of the following represents Anna's weight in pounds?

Short answer

Anna's weight is \( \frac{n - m}{2} \) pounds.

Step-by-step solution

- Define the variables

Let Anna's weight be represented by the variable \( A \) (in pounds). As Susan weighs \( m \) pounds more than Anna, Susan's weight can be represented as \( A + m \).

- Formulate the equation

Given that together Anna and Susan weigh a total of \( n \) pounds, the equation representing this situation can be written as: \[ A + (A + m) = n \]

- Simplify the equation

Combine the terms on the left side of the equation: \[ 2A + m = n \]

- Solve for Anna's weight

Isolate \( A \) by solving the equation: \[ 2A = n - m \] \[ A = \frac{n - m}{2} \]

Key concepts

variable representation

In algebra, a variable is a symbol used to represent unknown values. Variables help us translate real-world situations into mathematical expressions and equations.
Let's break down the weight problem.
To start, we need to identify the unknowns in our scenario.

• Anna's weight is one unknown, so we use the variable A to represent it.
• Susan's weight is another unknown, but we know it is m pounds more than Anna's. Therefore, we represent Susan's weight as A + m.

By expressing Susan's weight in relation to Anna’s weight, we simplify the problem and prepare to formulate an equation.

formulating equations

Formulating equations is essential when translating words into mathematical statements.
For the given problem:

• We know Anna and Susan together weigh n pounds.
• Express Anna's weight as A and Susan's weight as A + m.

We can then write an equation representing their combined weight:
\[ A + (A + m) = n \]
This equation captures the total weight of Anna and Susan. By formulating this step, we link the variables to the specific conditions described in the problem.

solving equations

Once we have formulated our equation, we need to solve for the unknown variable.
Let's solve the equation step-by-step:

• Start with the equation: \[ A + (A + m) = n \]
• Combine like terms on the left side: \[ 2A + m = n \]
• Isolate the variable A by moving other terms to the right side: \[ 2A = n - m \]
• Finally, solve for A by dividing both sides by 2: \[ A = \frac{n - m}{2} \]

This final equation, \[ A = \frac{n - m}{2} \], represents Anna's weight. By following these steps, we systematically solve for the variable, which makes complex problems more manageable.