Question 390691
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Let's begin with your last question because the answer is fundamental to the entirety of K-12 mathematics education.  The answer is simple:  You learn how to solve problems.  In fact, learning how to solve problems is the goal of ALL elementary and secondary education with the exception of the study of the English language.  The study of our language provides us with the ability to communicate the problems and their solutions to others.


You don't need two independent equations for this problem because one of the unknown ages can be expressed in terms of the other.  Let *[tex \Large x] represent Laura's age.  Then, because we know that Amy is three years older than Laura, we can represent Amy's age by *[tex \Large x\ +\ 3].


Then we can say that the product of their ages is *[tex \LARGE x(x\ +\ 3)] and two times the sum of their ages is *[tex \LARGE 2\left(x\ +\ (x\ +\ 3)\right)]


Now, if your 5th grader knows how to use the distributive property, collect terms, put a quadratic equation into standard form, determine the factors of a quadratic trinomial with integer factors, and apply the Zero Product Rule, then your student is home free.  If the student is unable to do any of these things, then one of the following is true:  1. The student has fallen behind the rest of the class, or 2.  The problem is inappropriate for this student's ability level.


My recommendation is that you consult with your student's teacher regarding that teacher's expectations for your student's current ability level and to develop a strategy to correct any deficiencies before the student begins to fail completely.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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