A woodworker starts with a wooden board of length L inches. After cutting off a piece meas… — ACT

A woodworker starts with a wooden board of length $L$ inches. After cutting off a piece measuring $16.5$ inches to build a shelf bracket, the remaining portion of the board is $48.5$ inches long. Which of the following equations can be used to find $L$ , the original length of the wooden board in inches?

$L - 16.5 = 48.5$ Answer
B
$L + 16.5 = 48.5$
C
$16.5L = 48.5$
D
$\frac{L}{16.5} = 48.5$
E
$48.5 - L = 16.5$

Answer

L - 16.5 = 48.5

The original length of the board is

L

inches. Cutting off a piece measuring

16.5

inches decreases the total length by

16.5

, which is written algebraically as

L - 16.5

. Since the remaining length is given as

48.5

inches, setting these equal produces the equation

L - 16.5 = 48.5

Step-by-Step Solution

Identify the given variables and quantities in the scenario

Initial length =

L

, length cut off =

16.5

, remaining length =

48.5

Establishing clear variables allows systematic setup of the algebraic model.

Translate the physical action into a mathematical operation

Cutting off a piece represents subtraction from the starting quantity:

L - 16.5

Removal of a part from a whole corresponds to subtraction.

Equate the expression for remaining length to the given remaining value

L - 16.5 = 48.5

The remaining length after cutting is stated to be

48.5

inches.

Key Concept

Translating verbal removal scenarios into one-step subtraction equations

Estimated Time:1m 0s

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