1) Two years ago, the age of a father was three and a half times the age of his
daughter then. Six years hence, the age of father will be ten years more than twice
the age of his daughter then. Find their present ages.
(1) Let the present age of the father be x years and that of his daughter be y years.
(2) Form two equations from the given conditions.
(3) Solve the equations and find the answer.
Answers
present age of Father = 44 Years & Daughter = 14 Years
Step-by-step explanation:
Let the present age of the father be x years and that of his daughter be y years.
Two years ago age of father = x - 2
Two years ago age of daughter = y - 2
Two years ago age of a father was three and a half times the age of his daughter
=> x - 2 = (7/2)(y - 2)
=> 2x - 4 = 7y - 14
=> 2x - 7y = - 10 Eq1
Six years hence, the age of father = x + 6
Six years hence, the age of Daughter = y +6
Six years hence, the age of father will be ten years more than twice
the age of his daughter then
=> x + 6 = 2(y + 6) + 10
=> x - 2y = 16 Eq2
Eq1 - 2 * eq2
=> -3y = -42
=> y = 14
x - 2*14 = 16
=> x = 44
present age of Father = 44 Years
Present age of Daughter = 14 Years
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Answer:
Step-by-step explanation:
Let the present age of the father be x years and that of his daughter be y years.
Two years ago age of father = x - 2
Two years ago age of daughter = y - 2
Two years ago age of a father was three and a half times the age of his daughter
=> x - 2 = (7/2)(y - 2)
=> 2x - 4 = 7y - 14
=> 2x - 7y = - 10 Eq1
Six years hence, the age of father = x + 6
Six years hence, the age of Daughter = y +6
Six years hence, the age of father will be ten years more than twice
the age of his daughter then
=> x + 6 = 2(y + 6) + 10
=> x - 2y = 16 Eq2
Eq1 - 2 * eq2
=> -3y = -42
=> y = 14
x - 2*14 = 16
=> x = 44
present age of Father = 44 Years
Present age of Daughter = 14 Years