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 initial length \( L \) minus the removed length (3.6 meters) equals the remaining length (4.73 meters). So the appropriate form is subtraction.

Step2: Fill in the blanks

Using the subtraction form \( \square - \square=\square \), we substitute \( L \) (initial length), 3.6 (removed length), and 4.73 (remaining length). So the equation is \( L - 3.6 = 4.73 \).

Part (b)

Step1: Solve for \( L \)

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

$$ L - 3.6 + 3.6 = 4.73 + 3.6 $$

Step2: Calculate the result

Simplifying the right - hand side: \( 4.73+3.6 = 8.33 \), so \( L = 8.33 \).

Answer:

s:
(a) The equation is \( \boldsymbol{L - 3.6 = 4.73} \) (using the \( \square - \square=\square \) form with \( L \) in the first blank, 3.6 in the second blank, and 4.73 in the third blank).
(b) The length of the rope at the beginning is \(\boldsymbol{8.33}\) meters.