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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.

Answer
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

3q = 675

q = 225

q = 15

Since p = 3q

p = (3)(15) = 45

The father is 45 , the son is 15.

Algebra

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