Question:
An electric cable cost 200 rupees.If the cable was 3 metres longer and each metre of cable cost rupee 2 less, the cost of cable would have unchanged. Represent the above situation in the form of a quadratic equation.
Answer:
Let the length of the piece of electric cable = x
Then cost per meter = 200/x
Now, length of electric cable = x + 3
Given, cost of the piece of the electric cable is unchanged
So, new cost per meter = 200/(x + 3)
According to question,
200/x - 200/(x + 3) = 2
=> {200(x + 3) - 200x}/{x(x + 3)} = 2
=> 200x + 600 - 200x = 2x(x + 3)
=> 600 = 2(x2 + 3x)
=> x2 + 3x = 600/2
=> x2 + 3x = 300
=> x2 + 3x - 300 = 0
This is the required equation.
Question: An electric cable cost 200 rupees.If the cable was 5 meters longer and each meter of cable cost rupee 2 less,
the cost of cable would have unchanged. Represent the above situation in the form of a quadratic equation.
Solu: When we solve this question as explained above, then we find the equation
x2 - 5x - 500 = 0
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