SOLUTION: The length of Jim's leader is always 2 feet shorter than the length of his fishing rod. If the product of the length of the leader and the length of the rod equals the strength of

Algebra.Com
Question 238098: The length of Jim's leader is always 2 feet shorter than the length of his fishing rod. If the product of the length of the leader and the length of the rod equals the strength of his line in pounds and he uses a 16-lb line, what is the length of his leader?
Answer by Stitch(470)   (Show Source): You can put this solution on YOUR website!
Let X = the length of the rod
Let Y = the length of the leader
Equation 1:
Equation 2:
Using equation 1, plug (X - 2) into equation 2 for Y

Rewrite the equation
Subtract 16 form both sides
Then you need to use the quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=68 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 5.12310562561766, -3.12310562561766. Here's your graph:

Since you can not have a negative length, the 5.123 is the only rational answer.
But remember that 5.123 is the length of the rod.
To find the length of the leader, plug 5.123 into equation 1 for X
Equation 1:


The leader = 3.123ft
RELATED QUESTIONS

The length of Jims leader is always 2 feet shorter than the length of his fishing rod. If (answered by Nate)
The lenght of Jim's leader is always 2 feet shorter than lenght of this fishing rod.If... (answered by stanbon)
36ft fishing line is cut to where the longer length is 6ft longer than the shorter... (answered by mary164)
A piece of iron rod costs P60. If the rod was 2 meter shorter and each meter costs P1... (answered by josgarithmetic,ikleyn)
a fishing line x=7 feet long is cut into two pieces, one shorter. Express the length of... (answered by richwmiller,jsmallt9)
Application Problems: A fishing line 3 ft. long is cut into two pieces, one shorter... (answered by stanbon)
From a length of rod 600cm in length, 25 pieces are cut off, each 1 cm longer than the... (answered by josgarithmetic)
a leader inclined at an angle of 36° to the horizontal leans against a vertical pole. if (answered by ikleyn,math_tutor2020)
A rectangular Home lot has an area of 240 ft.². it’s width is shorter than its length by (answered by josgarithmetic)