Writing Equations from Word Problems 1

Front

What is the general form of a linear equation used to represent a total cost that includes a fixed fee and a variable cost per unit?

Back

y = mx + b, where y is the total cost, m is the variable cost per unit, x is the number of units, and b is the fixed fee.

Front

How do you represent a situation where one quantity is a certain amount greater than another quantity in an equation?

Back

You can represent it as x + k = y, where x is the smaller quantity, k is the amount greater, and y is the larger quantity.

Front

What is the equation to find the total cost of multiple items when there is a fixed cost and a variable cost per item?

Back

Total Cost = Fixed Cost + (Cost per Item * Number of Items) or y = b + mx.

Front

How can you set up an equation to compare two different purchasing options to find when they cost the same?

Back

Set the total cost equations of both options equal to each other and solve for the variable.

Front

What does the variable 'x' typically represent in application-based word problems involving cost?

Back

The variable 'x' usually represents the number of items or units being purchased.

Front

In the context of a word problem, how do you identify the fixed cost?

Back

The fixed cost is the amount that does not change regardless of the number of items purchased, often stated as a flat fee.

Front

What is the significance of the coefficient in front of the variable in a cost equation?

Back

The coefficient represents the cost per unit of the item being purchased.

Front

How do you translate a word problem into a mathematical equation?

Back

Identify the quantities involved, determine the relationships between them, and express these relationships using variables and constants.

Front

What is the role of the constant term in a linear equation representing a total cost?

Back

The constant term represents the fixed costs that are incurred regardless of the number of items purchased.

Front

How do you determine the height of one object when given the combined height of two objects and their height difference?

Back

Set up an equation based on the total height and the difference, then solve for the unknown height.