Word Problems: Variables on Both Sides

Front

What is a variable in a mathematical equation?

Back

A symbol used to represent an unknown value in an equation.

Front

What does it mean to solve an equation with variables on both sides?

Back

It means to find the value of the variable that makes both sides of the equation equal.

Front

How do you isolate a variable in an equation?

Back

By performing inverse operations to get the variable alone on one side of the equation.

Front

What is the first step in solving a word problem involving two rates?

Back

Identify the rates and set up an equation based on the information given.

Front

If two taxi companies charge different rates, how can you find when their costs are equal?

Back

Set up an equation where the total costs of both companies are equal and solve for the variable representing miles.

Front

What is the significance of the entry fee in a rental problem?

Back

It is a fixed cost that must be added to the variable cost based on usage (e.g., miles driven).

Front

How do you determine which option is cheaper in a word problem?

Back

Calculate the total cost for each option and compare the results.

Front

What does 'no solution' mean in the context of an equation?

Back

It means that there is no value for the variable that can satisfy the equation.

Front

What is the formula to calculate total cost in a rental scenario?

Back

Total Cost = Fixed Fee + (Variable Rate × Number of Units Used).

Front

How can you represent a word problem algebraically?

Back

By defining variables for unknowns and translating the problem into an equation.