Question

product of pragati's age 2 years ago and 3 years hence is 84. find her present age.

Answer 1

87 is the answer because we have to plus 3 in 84 to find her present age

Answer 2

Answer:

Pragati's present age is 9 years.

Step-by-step-explanation:

$Let \: Pragati's \: present \: age \: be \: x \: years.$

$Her \: age \: 2 \: years \: ago \: was \: ( x - 2 ) \: years \: and \: her \: age \: 3 \: years \: from \: now \: will \: be \: ( x + 3 ) \: years.$

$From \: the \: given \: condition,$

$( x - 2 )\times( x + 3 ) = \: 84\\ \\</p><p> </p><p>\therefore x ( x + 3 ) - 2 ( x + 3 ) = 84 \\ \\ </p><p></p><p>\therefore x^{2} + 3x - 2x - 6 - 84 =0 \\ \\ </p><p></p><p>\therefore x^{2} + x - 90 = 0 \\ \\ </p><p></p><p>\therefore x^{2} + 10x - 9x - 90 = 0 \\ \\ </p><p></p><p>\therefore x ( x + 10 ) - 9 ( x + 10 ) = 0 \\ \\ </p><p></p><p>\therefore ( x + 10 ) \: ( x - 9 ) =0 \\ \\ </p><p></p><p>\therefore x + 10 = 0 \: \: OR \: \: x - 9 = 0 \\ \\ </p><p></p><p>\therefore x = - 10 \: \: OR \: \: x = 9$

$But \: the \: age \: cannot \: be \: negative.$

$\therefore x = - 10 \: is \: unacceptable. \\ \\ </p><p></p><p>\therefore \: \boxed{x = 9 }$

$Ans.: Pragati's \: present \: age \: is \: 9 \: years.$

Additional Information:

Steps to solve word problems based on quadratic equations:

1. Convert the given word problem into symbolic language ( use variables / alphabets ) by identifying the given conditions in the problem.

2. Solve the quadratic equation formed.

3. Convert the solution of the equation into words.

NOTE: The appropriate solution which satisfies the given conditions should be considered.