Word Problems: Variables on Both Sides

Front

What is a variable in an equation?

Back

A symbol, often represented by a letter, that stands for a number that can change or vary.

Front

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

Back

Identify the quantities involved, assign variables to unknowns, and express relationships using mathematical operations.

Front

What does it mean to have variables on both sides of an equation?

Back

It means that the unknowns (variables) appear on both sides of the equal sign, requiring manipulation to isolate the variable.

Front

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

Back

Combine like terms and isolate the variable by performing inverse operations on both sides of the equation.

Front

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

Back

Identify the fixed costs and variable costs associated with each option.

Front

In the equation 150 + 24x = 180 + 20x, what do the terms represent?

Back

150 is the fixed cost of the Xbox, 24x is the cost of x games, 180 is the fixed cost of the Playstation, and 20x is the cost of x games for the Playstation.

Front

What is the significance of the solution to an equation in a word problem?

Back

The solution represents the value of the variable that makes the two sides of the equation equal, often indicating a point of balance or equivalence.

Front

How do you determine which option is the better deal in a word problem?

Back

Calculate the total cost for each option based on the given quantities and compare the results.

Front

What does it mean if an equation has no solution?

Back

It means that there is no value for the variable that can satisfy the equation, indicating that the scenarios described are not possible.

Front

What is a fixed cost in a word problem?

Back

A cost that does not change regardless of the quantity purchased, such as membership fees or initial charges.