5. A 14-inch piece of wood is going to be cut so that one of the pieces is 4 inches shorter than the other. How long is the shorter piece?
Answer: A
The shorter piece is 5 inches long.
To find the length of the shorter piece, we can set up an equation. Let the length of the longer piece be \(x\). The shorter piece is then \(x - 4\). Together, these pieces equal 14 inches, so the equation is \(x + (x - 4) = 14\). Solving this gives \(x = 9\) and the shorter piece is \(9 - 4 = 5\) inches.
A) 5 inches
This option is correct because when the longer piece is 9 inches, subtracting 4 inches gives the shorter piece a length of 5 inches. This satisfies the condition that the total length of both pieces is 14 inches.
B) 9 inches
This option is incorrect because if the shorter piece were 9 inches, that would make the longer piece 13 inches (9 + 4), resulting in a total of 22 inches, which exceeds the original 14-inch length.
C) 4 inches
This option is also incorrect because if the shorter piece were 4 inches, the longer piece would need to be 8 inches (4 + 4). Together, these add up to 12 inches, which is less than the required 14 inches.
D) 10 inches
This option is incorrect as well. If the longer piece were 10 inches, the shorter piece would then be 6 inches (10 - 4). The total would be 16 inches, which again exceeds the 14-inch length.
Conclusion
The correct answer, 5 inches, accurately reflects the mathematical relationship established in the problem. All other options fail to meet the condition of totaling 14 inches or do not meet the specified relationship between the lengths of the two pieces. Thus, option A is definitively the right choice.