Introduction:
A person cuts a rope into two pieces that are equal in length. The first piece is 4 times the length of the person’s forearm, minus 1 inch. The second piece is 3 times the length of the person’s forearm, plus 15 inches. For purposes of this question, consider that the standard definition of a forearm is the portion of the arm from the elbow to the wrist.
Task:
A. Construct the two linear equations that represent the situation in the given using x as the variable for the person’s forearm and y for the other unknown.
The variable x represent length of the person’s forearm and y represent the length of the piece of the rope. Therefore,
(1)
(2)
B. Solve the two linear equations you constructed to find the length of the person’s forearm.
1. Find the solution both algebraically and graphically.
2. Show your work both algebraically and graphically. Scale your graph appropriately to view the solution.
Substituting value of y from equation 1 into equation (2)
Therefore, the length of the person’s forearm is equal to 16 inches and the length of the piece of the rope is 63 inches.
C. Briefly discuss whether your answer makes sense in the context of the original problem.
Typically, a person’s forearm length is in between 8 to 12 inches. Therefore, 16 inches is too long to be reasonable.
No, my answer that the length of person’s forearm is equal to 16 inch does not make sense in the context of the original problem.
