Solving Equations - Word Problems

Front

What is the general form of a linear equation used to represent a word problem involving costs and revenues?

Back

The general form is: Total Costs = Total Revenue, which can be expressed as C + mx = px, where C is fixed costs, m is variable cost per unit, p is price per unit, and x is the number of units.

Front

How do you set up an equation for a word problem involving a fixed cost and a variable cost?

Back

Identify the fixed cost and the variable cost per unit, then express the total cost as the sum of the fixed cost and the product of the variable cost and the number of units.

Front

In the context of word problems, what does 't' typically represent?

Back

In word problems, 't' often represents the number of items or units being considered, such as the number of teddy bears sold.

Front

What is the first step in solving a word problem that requires forming an equation?

Back

The first step is to carefully read the problem to identify the quantities involved and the relationships between them.

Front

How can you determine the total number of students if some are returning home and others are staying?

Back

Subtract the number of students returning from the total number of students to find those staying, then divide by the capacity of each cabin to find the number of cabins needed.

Front

What does the equation 0.5x + 4 = 12 represent in a word problem?

Back

This equation represents a situation where half of a weekly allowance (x) plus $4 earned from washing a car equals $12, which is the total amount Imani has.

Front

How do you interpret the phrase '10 less than one third of my age' in an equation?

Back

This phrase can be expressed as (1/3)A - 10, where A represents the age.

Front

What is the significance of the coefficients in a linear equation derived from a word problem?

Back

Coefficients represent the rate of change or the cost per unit in the context of the problem, indicating how much the total changes with each additional unit.

Front

How do you find the number of items needed to meet a specific condition in a word problem?

Back

Set up an equation based on the conditions given in the problem, then solve for the variable representing the number of items.

Front

What is the relationship between total costs and total revenue in a business context?

Back

Total costs must equal total revenue for a business to break even; this is often represented in equations to find the number of units needed to sell.