Variables on Both Sides Word Problems

Front

What is a variable in an equation?

Back

A variable is a symbol used to represent an unknown value in an equation, often denoted by letters such as x or y.

Front

How do you set up an equation for a word problem involving costs?

Back

Identify the costs associated with each option, express them as equations, and set them equal to each other to find the point of equivalence.

Front

What does it mean for two costs to be equal in a word problem?

Back

It means that the total expenses for both options will be the same at a certain point, allowing for comparison.

Front

How do you solve an equation with variables on both sides?

Back

To solve, first simplify both sides if necessary, then isolate the variable by moving terms involving the variable to one side and constant terms to the other.

Front

What is the significance of the intersection point in a cost comparison problem?

Back

The intersection point represents the quantity at which the total costs of two different options are equal.

Front

How can you determine the number of items needed for two costs to be equal?

Back

Set up an equation based on the costs, solve for the variable representing the number of items, and interpret the solution.

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed, typically in the form y = mx + b.

Front

What is the formula for calculating total cost in a word problem?

Back

Total cost can be calculated using the formula: Total Cost = Fixed Cost + (Variable Cost per Item × Number of Items).

Front

How do you interpret the solution of a variable equation in a real-world context?

Back

The solution represents the quantity or value that satisfies the conditions of the problem, often indicating how many items or units are needed.

Front

What is the role of constants in equations?

Back

Constants are fixed values that do not change, representing fixed costs or quantities in equations.