A piece of iron rod costs $60. If the rod was 2 meters shorter and each meter costs $1 more, the cost would remain unchanged. What is the length of the rod?
Answers
⇒SOLUTION:-
⇁Let x be the length of the given rod.
⇁Then the length of the rod 2 meter shorter is (x - 2) and the total cost of both the rods is $60 (Because cost would remain unchanged).
⇁Cost of one meter of the given rod is
= 60 / x
⇁Cost of one meter of the rod which is 2 meter shorter is
= 60 / (x - 2)
Given : If the rod was 2 meter shorter and each meter costs $1 more.
That is, 60/(x-2) is $1 more than 60/x.
⇢ [60 / (x - 2)] - [60 / x] = 1
Simplify.
⇢ [60x - 60(x - 2)] / [x(x - 2)] = 1
⇢ [60x - 60x + 120] / [x² - 2x] = 1
⇢ 120 / (x² - 2x) = 1
⇢ 120 = x² - 2x
⇢ 0 = x²+ 2x - 120
⇢ x² + 2x - 120 = 0
⇢ (x + 10)(x - 12) = 0
⇢ x = - 10 or x = 12
⇁Because length can not be a negative number, we can ignore "- 10".
So, the length of the given rod is 12 m.