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The square of Mark's age 3 years ago is 6 times the age he will be in 9 years. What is his age now?
Solution:
Let us express the given statements into algebraic expressions.
Let us assume the present age of Mark is x years.
3 years ago Mark’s age will be x - 3 years.
9 years from now Mark will be x + 9 years old
According to the question,
(x - 3)2 = 6(x + 9)
⇒ Now solve for x
⇒ x2 + 32 - 2(3)(x) = 6x + 54
⇒ x2 + 9 - 6x = 6x + 54
⇒ x2 - 12x - 45 = 0
⇒ x2 -15x + 3x - 45 = 0
⇒ x(x - 15) + 3(x - 15) = 0
⇒ (x + 3)(x - 15) = 0
⇒ x = -3, 15
Age cannot be negative therefore the present age of Mark will be 15 years old.
The square of Mark's age 3 years ago is 6 times the age he will be in 9 years. What is his age now?
Summary:
If the square of Mark's age 3 years ago is 6 times the age he will be in 9 years then the present age of Mark will be 15 years old.
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