Find the present ages of Angie and Paul - problem solving
Problem:
Angie is 4 years older than Paul. Find their present ages if the product of Angie's age 6 years from now and Paul's age 5 years ago is 700.
This problem can actually be solved either by using quadratic formula or by factoring method. These methods are one of the four ways in solving quadratic equations. In today's post shows only the method of solving quadratic equation by factoring.
It is important that you have a good background on those methods of solving quadratic equations because most problems that we encounter in life are quadratic in nature.
In Algebra we usually represent the unknown with variables. If we can put those variables in terms of quadratic equations, only then we may be able to find values for that variable that would make the equation true . These values are what we called solutions to the problem. And one way of finding the solutions of a quadratic equation is by factoring method.
The standard equation
where a ≠ 0 can be factored as the product of two linear factors. We then use the zero product property to determine the solution after factoring.
Before we proceed, let us define first the following terms.
Definition of Terms:
• Quadratic Equation - any equation that can be written in the form of 
where a, b and c are real numbers and a ≠ 0.
• Factoring - the process of finding the two linear factors or what to multiply to get the quadratic.
• Zero Product Property - states that, " If p and q are real numbers and pq = 0, then
either p = 0 or q = 0 or both are zero.
• Solution - values or numbers that satisfy the equation.
These values are what we called solutions to the problem.
Let us now solve the problem:
"Angie is 4 years older than Paul. Find their present ages if the product of Angie's age 6 years from now and Paul's age 5 years ago is 700."
Remember, our goal is to come up with a quadratic equation out from the given problem.
So, let x = Paul's present age.
x + 4 = Angie's present age
Illustration:
Solution:
We now obtained the value x = 25.
We reject x = - 30 since there is no negative age.Checking:
Bravo!!!
The obtained value satisfies the equation.Alright! Let us first recall how we obtained the value x = 25 before giving a conclusion.
Solving quadratic equations by factoring
- Rewrite the equation in its general form
- Factor the left member of the equation
- Equate each factor to zero
- Solve for x
Conclusion:
Recall that
x = Paul's present age
x + 4 = Angie's present age.
Therefore if x = 25, then Paul's present age is 25 while Angie's present age is 29.
Problem solved!
the more i can't relate with numbers on this cold, stormy weather, adto tas skol ron?