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# Algebra/Word_problem

Question
I find the difficult to interprete and solve this question: A man is q years old while his son is p years old. The sum of their ages is equal to twice the difference of their ages. The product of their ages is 675. Write down the equations connecting their ages and solve the equations in order to find the ages of the man and his son.

The sum of their ages is equal to twice the difference if their ages

p + q = 2(p-q)

The product of their ages is 675

pq = 675

Solve the two equations :

p + q = 2(p-q)

pq = 675

Simplify the first equation

p+q = 2p-2q

3q = p

Substitute 3q in for p in the second equation

pq = 675

(3q)(q) = 675

3q² = 675

q² = 225

q = 15

Since p = 3q

p = (3)(15) = 45

The father is 45 , the son is 15.

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Algebra

Volunteer

#### Socrates

##### Expertise

Any questions on High School Algebra, College Algebra, Abstract Algebra. I can help with word problems, solving equations, trigonometry, inequalities, Gaussian Elimination, Linear Algebra, groups, fields, you name it!

##### Experience

Ph.D. in Mathematics, specialist in Algebra. I have taught High School students and college students at three state universities.

Organizations
Mathematical Association of America. American Mathematical Society.

Publications
Regular contributions to the problems section of the American Mathematical Monthly journal.

Education/Credentials
B.S., M.S., Ph.D.