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Five year ago , a woman's age ( in years ) was the square of her son's age . Ten years from now , her age will be twice that of her son's age find - A- the age of the son five years ago B- the present age of the women ( quadratic equation )?
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Problem Analysis:
Let's assume the present age of the woman is W and the present age of her son is S. We are given two pieces of information:
1. Five years ago, the woman's age was the square of her son's age: W - 5 = (S - 5)^2.
2. Ten years from now, her age will be twice that of her son's age: W + 10 = 2(S + 10).
We need to find the age of the son five years ago (S - 5) and the present age of the woman (W).
Solution:
Step 1: Age of the Son Five Years Ago (S - 5)
To find the age of the son five years ago, we can substitute the given equation from the first piece of information:
W - 5 = (S - 5)^2
Taking the square root of both sides:
√(W - 5) = S - 5
Adding 5 to both sides:
S - 5 + 5 = √(W - 5) + 5
S = √(W - 5) + 5
Therefore, the age of the son five years ago is given by S - 5 = (√(W - 5) + 5) - 5 = √(W - 5).
Step 2: Present Age of the Woman (W)
To find the present age of the woman, we can substitute the given equation from the second piece of information:
W + 10 = 2(S + 10)
Simplifying the equation:
W + 10 = 2S + 20
Subtracting 20 from both sides:
W + 10 - 20 = 2S + 20 - 20
W - 10 = 2S
Dividing both sides by 2:
(W - 10) / 2 = (2S) / 2
(W - 10) / 2 = S
Substituting the value of S from Step 1:
(W - 10) / 2 = √(W - 5)
Squaring both sides:
[(W - 10) / 2]^2 = (√(W - 5))^2
(W - 10)^2 / 4 = W - 5
Expanding and simplifying:
(W^2 - 20W + 100) / 4 = W - 5
W^2 - 20W + 100 = 4W - 20
Rearranging the equation:
W^2 - 20W - 4W + 100 + 20 = 0
W^2 - 24W + 120 = 0
This is a quadratic equation. We can solve it by factoring or using the quadratic formula.
Step 3: Solving the Quadratic Equation
To solve the quadratic equation W^2 - 24W + 120 = 0, we can first check if it can be factored.
The factors of 120 that add up to -24 are -12 and -10.
Therefore, the quadratic equation can be factored as:
(W - 12)(W - 10) =
Let's assume the present age of the woman is W and the present age of her son is S. We are given two pieces of information:
1. Five years ago, the woman's age was the square of her son's age: W - 5 = (S - 5)^2.
2. Ten years from now, her age will be twice that of her son's age: W + 10 = 2(S + 10).
We need to find the age of the son five years ago (S - 5) and the present age of the woman (W).
Solution:
Step 1: Age of the Son Five Years Ago (S - 5)
To find the age of the son five years ago, we can substitute the given equation from the first piece of information:
W - 5 = (S - 5)^2
Taking the square root of both sides:
√(W - 5) = S - 5
Adding 5 to both sides:
S - 5 + 5 = √(W - 5) + 5
S = √(W - 5) + 5
Therefore, the age of the son five years ago is given by S - 5 = (√(W - 5) + 5) - 5 = √(W - 5).
Step 2: Present Age of the Woman (W)
To find the present age of the woman, we can substitute the given equation from the second piece of information:
W + 10 = 2(S + 10)
Simplifying the equation:
W + 10 = 2S + 20
Subtracting 20 from both sides:
W + 10 - 20 = 2S + 20 - 20
W - 10 = 2S
Dividing both sides by 2:
(W - 10) / 2 = (2S) / 2
(W - 10) / 2 = S
Substituting the value of S from Step 1:
(W - 10) / 2 = √(W - 5)
Squaring both sides:
[(W - 10) / 2]^2 = (√(W - 5))^2
(W - 10)^2 / 4 = W - 5
Expanding and simplifying:
(W^2 - 20W + 100) / 4 = W - 5
W^2 - 20W + 100 = 4W - 20
Rearranging the equation:
W^2 - 20W - 4W + 100 + 20 = 0
W^2 - 24W + 120 = 0
This is a quadratic equation. We can solve it by factoring or using the quadratic formula.
Step 3: Solving the Quadratic Equation
To solve the quadratic equation W^2 - 24W + 120 = 0, we can first check if it can be factored.
The factors of 120 that add up to -24 are -12 and -10.
Therefore, the quadratic equation can be factored as:
(W - 12)(W - 10) =
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Five year ago , a woman's age ( in years ) was the square of her son's age . Ten years from now , her age will be twice that of her son's age find - A- the age of the son five years ago B- the present age of the women ( quadratic equation )?
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Five year ago , a woman's age ( in years ) was the square of her son's age . Ten years from now , her age will be twice that of her son's age find - A- the age of the son five years ago B- the present age of the women ( quadratic equation )? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Five year ago , a woman's age ( in years ) was the square of her son's age . Ten years from now , her age will be twice that of her son's age find - A- the age of the son five years ago B- the present age of the women ( quadratic equation )? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five year ago , a woman's age ( in years ) was the square of her son's age . Ten years from now , her age will be twice that of her son's age find - A- the age of the son five years ago B- the present age of the women ( quadratic equation )?.
Five year ago , a woman's age ( in years ) was the square of her son's age . Ten years from now , her age will be twice that of her son's age find - A- the age of the son five years ago B- the present age of the women ( quadratic equation )? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Five year ago , a woman's age ( in years ) was the square of her son's age . Ten years from now , her age will be twice that of her son's age find - A- the age of the son five years ago B- the present age of the women ( quadratic equation )? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five year ago , a woman's age ( in years ) was the square of her son's age . Ten years from now , her age will be twice that of her son's age find - A- the age of the son five years ago B- the present age of the women ( quadratic equation )?.
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