Writing Equations from Word Problems

Front

What is the first step in writing an equation from a word problem?

Back

Identify the variables and what they represent in the context of the problem.

Front

How do you represent a fixed cost in an equation?

Back

A fixed cost is represented as a constant term in the equation, such as 'C' in the equation C + mx, where C is the fixed cost.

Front

What does 'm' represent in the equation C + mx?

Back

In the equation C + mx, 'm' represents the variable cost per unit, such as cost per ride or cost per mile.

Front

How do you set up an equation to compare two different costs?

Back

Set the two cost expressions equal to each other, such as C1 + m1x = C2 + m2x.

Front

What is the significance of the variable 'x' in equations derived from word problems?

Back

The variable 'x' typically represents the quantity of items or units being considered, such as the number of rides or miles.

Front

How can you determine the number of items purchased from a total cost?

Back

You can set up an equation where the total cost equals the sum of fixed costs and variable costs, then solve for the variable representing the number of items.

Front

What does it mean if an equation has no solution in the context of a word problem?

Back

It means that the conditions described in the problem cannot be satisfied, indicating that the scenarios being compared are not possible.

Front

How do you interpret the slope in a cost equation?

Back

The slope represents the rate of change in cost per unit, indicating how much the total cost increases with each additional unit.

Front

What is the purpose of using equations in word problems?

Back

Equations help to model real-world situations mathematically, allowing for analysis and solution of problems.

Front

What is a common mistake when writing equations from word problems?

Back

A common mistake is misinterpreting the relationships between quantities, leading to incorrect equations.