Question

select the correct answer from each drop - down menu. a machine cuts a strip of carpet into two pieces. the length of the smaller piece is 5 meters greater than \\(\frac{1}{4}\\) the length of the larger piece. if the length of the smaller piece is 12 meters, the length of the bigger piece is \\(28\\) meters and the total length of the carpet is \\(\boldsymbol{\text{drop - down menu}}\\) meters. reset next drop - down menu options: 25.5, 26, 32, 40

Explanation:

Step1: Verify the length of the larger piece

Let the length of the larger piece be \( x \) meters. The length of the smaller piece is given by the equation: \( 12=\frac{1}{4}x + 5 \).
Subtract 5 from both sides: \( 12 - 5=\frac{1}{4}x \), so \( 7=\frac{1}{4}x \).
Multiply both sides by 4: \( x = 28 \) meters (which matches the given value for the larger piece).

Step2: Calculate the total length

The total length of the carpet is the sum of the lengths of the smaller and larger pieces.
Smaller piece length = 12 meters, larger piece length = 28 meters.
Total length \( = 12 + 28 = 40 \) meters.

Answer:

40