1. A rope 75 feet long is cut into two pieces where one is 11 feet longer than the other. Find their lengths.
Solutions:
Let x be the longer piece and y be the other.
Thus x + y = 75
x = 11 + y; since the other is 11 feet longer than the other
Thus, we have 2 equations and two unknowns:
\(x + y = 75\) ; eq (1)
\(x = 11 + y\) ; eq (2)
\(\left( {11 + y} \right) + y = 75\) ; Substitute equation 2 to equation 1.
\(2y = 75 - 11\)
\(y = \frac{{64}}{2}\)
\(y = 32\)
\(x = 11 + 32\)
\(x = 43\)
Therfore the lengths are 43 feet and 32 feet.