Problem solving through equations is a method of solving problems by using algebraic equations. In math, we often use equations to represent a situation where we know some of the values, but not all of them.
To solve a problem through equations, we typically follow these steps:
Read and understand the problem: To solve a problem through equations, you first need to read and understand the problem. Identify what the problem is asking you to find and what information is given.
Define your variables: Once you understand the problem, define your variables. Variables are letters or symbols that represent the unknown quantities in the problem. For example, if a problem asks you to find the length of a rectangle, you might use "l" to represent the length.
Write an equation: Once you have defined your variables, write an equation that represents the problem. This equation should use the variables you defined in step 2, as well as any given values from the problem.
Solve the equation: Once you have written the equation, solve it to find the value of the unknown variable. This might involve using the sum and product rules, or the quadratic formula, depending on the type of equation.
Check your answer: Finally, check your answer to make sure it makes sense in the context of the problem.
For example, let's say we have a problem that asks us to find the length of a rectangle. We know that the width of the rectangle is 3 and the area of the rectangle is 12. We can use the following steps to solve the problem through equations:
Read and understand the problem: We want to find the length of a rectangle, given its width and area.
Define your variables: Let "l" represent the length of the rectangle.
Write an equation: The area of a rectangle is given by the formula A = lw. We know that the width is 3 and the area is 12, so we can write:
12 = 3l
Solve the equation: To solve for "l", we can divide both sides of the equation by 3: 12/3 = l
4 = l
So the length of the rectangle is 4.
Check your answer: We can check our answer by using the formula for the area of a rectangle: A = lw
A = 3(4)
A = 12
This checks out, so we know our answer is correct.