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

Explanation:

Step1: Define variables

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

Step2: Solve for \( x \)

Subtract 5 from both sides of the equation:
\( 12 - 5=\frac{1}{4}x \)
\( 7=\frac{1}{4}x \)
Multiply both sides by 4 to solve for \( x \):
\( x = 7\times4 = 28 \)

Step3: Find total length

The total length of the carpet is the sum of the lengths of the two pieces. So total length \(= 12 + 28=40\)? Wait, no, wait. Wait, the options for the first drop - down: let's check again. Wait, maybe I made a mistake. Wait, the equation: smaller piece is 5 meters greater than 1/4 the length of the larger piece. So smaller = (1/4)larger +5. Smaller is 12. So 12=(1/4)larger +5. Subtract 5: 7=(1/4)larger. Multiply by 4: larger =28. Then total length is 12 +28 =40. But the options for the first drop - down: 13.5,14,20,28. So the length of the bigger piece is 28 meters. Then total length is 12 +28 =40? Wait, but maybe the options for the second drop - down are not shown, but from the first part, the length of the bigger piece is 28 meters.

Answer:

For the length of the bigger piece: 28 meters. For the total length: 12 + 28 = 40 meters (assuming the second drop - down has 40 as an option, but based on the first part, the length of the bigger piece is 28 meters). So the length of the bigger piece is 28 meters.