Equation Word Problems

A word problem is a mathematical problem that is presented in the form of a narrative or story, requiring the reader to extract relevant information and formulate an equation to solve it.

Formulating an equation from a word problem involves translating the situation described in the problem into a mathematical expression that can be solved.

The total revenue (R) from selling items can be expressed as R = price per item (p) × number of items sold (n), or R = p × n.

Let x represent the number of children and y represent the number of adults. The total revenue can then be expressed as $$1.5x + 4y = total revenue$$ .

The slope indicates the rate of change of the dependent variable with respect to the independent variable. In word problems, it often represents a rate, such as speed or cost per item.

To find the number of items sold, rearrange the total revenue equation to isolate the variable representing the number of items.

The formula to calculate time (t) is t = distance (d) / rate (r). This is often used in problems involving speed or descent.

For a descending airplane, the equation can be set up as $$y = -rate \times time + initial height$$ , where 'rate' is the descent rate and 'initial height' is the starting altitude.

In a system of equations, the variables represent quantities that are interdependent, and the equations describe how these quantities relate to each other.

To solve for one variable, you can use substitution or elimination methods to isolate the variable in one of the equations.