### Math Notes

Subjects

#### Algebra Solutions

##### Topics || Problems

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.