How to Solve Word Problems by Finding Two-Variable Equations?

A step-by-step guide to solving word problems by finding two-variable equations

Here is a step-by-step guide on how to solve word problems by finding two-variable equations:

1. Read the problem carefully: Begin by reading the problem carefully to understand what is being asked. Identify the relevant variables and their relationships to each other.
2. Choose variables to represent the problem: Choose variables to represent the quantities involved in the problem. It’s common to use x and y as variables in two-variable equations, but other variables can also be used.
3. Identify the known quantities: Identify the quantities in the problem that are known, such as given values or constraints.
4. Identify the unknown quantities: Identify the quantities in the problem that are unknown, which are typically the values you are trying to solve for.
5. Write a two-variable equation: Write a two-variable equation that relates the known and unknown quantities. This equation should represent the problem in a way that can be solved algebraically.
6. Solve the equation: Use algebraic techniques to solve the equation for the unknown quantity. This may involve rearranging the equation, factoring, or using formulas.
7. Check your answer: Once you have solved for the unknown quantity, check your answer by plugging it back into the original equation and verifying that it makes sense in the context of the problem.
8. Interpret the solution: Finally, interpret the solution in the context of the problem. Make sure the answer makes sense and is reasonable given the known constraints and quantities.

Solving Word Problems by Finding Two-Variable Equations – Example 1

Solve the relationships in the word problem.
There are \(8\) cookies in a pack. Let \(p\) represent the number of packs and \(c\) represent the number of cookies. Find the number of cookies when \(p=2\).

Solution:

Look for relationships between the number of packs and cookies.
Find c by multiplying the number of packs by cookies.
So, \(8×2=16\)
\(c=16\)

Solving Word Problems by Finding Two-Variable Equations – Example 2

Solve the relationships in the word problem.
David rides the taxi for \(10\) minutes every day. \(d\) represents the number of days and \(m\) represents the total number of minutes David spends in the taxi. After two weeks how much time will he spend in the taxi?

Solution:

Look for relationships between the number of days and minutes.
He spends 10 minutes every day.
To know the total time after two weeks (14 days), multiply time by days.
So, \(10×14=140\)
\(t=140\)