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 \\(\boldsymbol{\text{dropdown}}\\) meters and the total length of the carpet is \\(\boldsymbol{\text{dropdown}}\\) meters. 13.5 14 20 28 reset

Explanation:

Step1: Define variable for larger piece

Let \( x \) be the length of the larger piece (in meters). The smaller piece length is given by the equation: \( \text{Smaller length} = \frac{1}{4}x + 5 \). We know the smaller piece is 12 meters, so substitute:
\( 12=\frac{1}{4}x + 5 \)

Step2: Solve for \( x \) (larger piece)

Subtract 5 from both sides:
\( 12 - 5=\frac{1}{4}x \)
\( 7=\frac{1}{4}x \)
Multiply both sides by 4:
\( x = 7\times4 = 28 \) meters (length of larger piece)

Step3: Find total length

Total length = smaller length + larger length = \( 12 + 28 = 40 \)? Wait, no, wait—wait, the drop - down for total? Wait, the first drop - down is for larger piece (28), then total length is \( 12 + 28=40 \)? But the options for the first drop - down: 13.5,14,20,28. So larger piece is 28. Then total length is \( 12 + 28 = 40 \)? Wait, maybe I misread. Wait, the problem says "the length of the bigger piece is [drop - down] meters and the total length of the carpet is [drop - down]". Wait, let's re - check the equation. Wait, the smaller piece is 5 meters greater than 1/4 the larger. So if larger is 28, 1/4 of 28 is 7, 7 + 5 = 12, which matches the smaller piece (12). So larger piece is 28. Then total length is 12+28 = 40? But the options for the first drop - down (bigger piece) are 13.5,14,20,28. So 28 is the larger piece. Then total length is 12 + 28 = 40. But maybe the second drop - down? Wait, the first drop - down (bigger piece) answer is 28. Then total length is 12+28 = 40, but let's check the steps again.

Wait, step1: Let \( x \) be larger piece. Smaller = (1/4)x + 5. Smaller is 12. So 12=(1/4)x + 5. Subtract 5: 7=(1/4)x. Multiply by 4: x = 28. So larger piece is 28. Then total length is 12 + 28 = 40. But the first drop - down (bigger piece) has 28 as an option. So for the first drop - down (bigger piece), the answer is 28. Then total length is 12+28 = 40. But let's confirm.

Answer:

First drop - down (length of bigger piece): 28 meters. Second drop - down (total length): 40 meters (but since the first drop - down options are 13.5,14,20,28, the bigger piece is 28, and total is 12 + 28 = 40). But based on the first drop - down, the answer for the bigger piece is 28.