Question
Cut a 10 ft long piece of wood into two pieces, so that one piece is 2 ft. longer than the other. Which of the following equations depicts the given situation?
x/2 = 10
x + 2 = 10
x = 10 + 2
2(x + 1) = 10
x/2 = 10
x + 2 = 10
x = 10 + 2
2(x + 1) = 10
Answers
GPT-4o mini
To model the situation described, let's define the lengths of the two pieces of wood.
Let \( x \) be the length of the shorter piece. According to the problem, the longer piece is 2 ft longer than the shorter piece, so the length of the longer piece can be expressed as \( x + 2 \).
The total length of the two pieces combined is 10 ft. Therefore, we can set up the equation:
\[
x + (x + 2) = 10
\]
This simplifies to:
\[
2x + 2 = 10
\]
However, if we look at the provided options, none of them appear to represent this equation directly.
Given the context of the options, the most relevant choice would be:
**None of the given equations accurately depict the situation.**
However, if one were to rearrange or simplify the derived equation, it would yield the correct total length equation. But based on the specific options provided, none represent the scenario correctly.
Let \( x \) be the length of the shorter piece. According to the problem, the longer piece is 2 ft longer than the shorter piece, so the length of the longer piece can be expressed as \( x + 2 \).
The total length of the two pieces combined is 10 ft. Therefore, we can set up the equation:
\[
x + (x + 2) = 10
\]
This simplifies to:
\[
2x + 2 = 10
\]
However, if we look at the provided options, none of them appear to represent this equation directly.
Given the context of the options, the most relevant choice would be:
**None of the given equations accurately depict the situation.**
However, if one were to rearrange or simplify the derived equation, it would yield the correct total length equation. But based on the specific options provided, none represent the scenario correctly.