Polynomial multiplication
Understand the Problem
The question is asking for the steps to perform polynomial multiplication and also relates to solving linear equations through word problems. It involves several multi-part questions including solving for ages and converting equations into standard form.
Answer
Abdul Hadi is $32$ years old and Abdullah is $10$ years old.
Answer for screen readers
Abdul Hadi is currently 32 years old, and Abdullah is currently 10 years old.
Steps to Solve
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Understanding the Problem Carefully read each question to identify the unknowns and conditions set by the problem. For questions involving ages, identify the relationships between the ages of the individuals mentioned.
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Define Variables Assign variables to the unknown quantities:
- For example, let $x$ represent the age of Abdul Hadi and $y$ represent Abdullah's age.
- Set Up Equations Translate the relationships and conditions into mathematical equations based on the information given:
- For example, if it states that "Abdul Hadi is 32 years old," then $x = 32$.
- Similarly, if "In two years, Abdul Hadi will be three times as old as Abdullah," translate that to $x + 2 = 3(y + 2)$.
- Combine Information to Form Linear Equations Use the information gathered to form linear equations:
- Aggregate all the information to write down all relevant equations.
- Solve the Equations Use methods such as substitution or elimination to solve the system of equations:
- Isolate one variable and substitute its value into the other equations.
- Check Your Work Verify your results by plugging the values back into the original conditions of the problem to ensure they hold true.
Abdul Hadi is currently 32 years old, and Abdullah is currently 10 years old.
More Information
This is a word problem involving linear equations that illustrates the relationships between the ages of two people over time. Setting up equations helps in finding the current ages based on given future conditions.
Tips
- Forgetting to account for future time adjustments when setting up equations.
- Misinterpreting the relationships between the variables, especially concerning older and younger.
- Failing to check the solution against the original problem conditions.
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