Question

at the beginning of a trick, a magician holds up a piece of rope. then she removes 3.6 meters from one of the ends. the length of the remaining rope is 4.73 meters.
(a) let l be the length of the rope at the beginning of the trick (in meters). write an equation that can be used to find l. first choose an appropriate form. then fill in the blanks with the letter l and the numbers 3.6 and 4.73.
○ □ + □ = □
○ □ − □ = □
○ □ × □ = □
○ □ ÷ □ = □
(b) solve your equation for l to find the length of the rope at the beginning of the trick.
□ meters

Explanation:

Part (a)

Step1: Analyze the relationship

The original length is \( L \), we remove 3.6 meters, and the remaining is 4.73 meters. So the operation is subtraction: original length minus removed length equals remaining length.

Step2: Form the equation

So the equation is \( L - 3.6 = 4.73 \), which corresponds to the \( \square-\square=\square \) option with \( L \), \( 3.6 \), and \( 4.73 \) in the blanks respectively.

Part (b)

Step1: Solve for \( L \)

To solve \( L - 3.6 = 4.73 \), we add 3.6 to both sides of the equation.

Step2: Calculate the value

\( L=4.73 + 3.6 \)
\( L = 8.33 \)

Answer:

(a) The appropriate equation is \( \boldsymbol{L - 3.6 = 4.73} \) (choosing the \( \square-\square=\square \) option with \( L \), \( 3.6 \), \( 4.73 \) in the blanks).
(b) The length of the rope at the beginning is \(\boldsymbol{8.33}\) meters.