Final answer:
To find the length of each piece of the ribbon, we can set up a proportion using the given ratios and solve for the missing term.
Step-by-step explanation:
Solve for the missing term:
To find the length of each piece of the ribbon, we can set up a proportion using the given ratios. We know that the
total length of the ribbon is 84 meters, and the ratio of the lengths for pieces x, y, and z is 4:2:1.
Let's set up the proportion as follows:
4x + 2x + x = 84
Simplifying the equation, we get:
7x = 84
To solve for x, divide both sides of the equation by 7:
x = 12
To find the length of each piece, we can substitute x back into the equation:
Length of piece x = 4x = 4(12) = 48 meters
Length of piece y = 2x = 2(12) = 24 meters
Length of piece z = x = 12 meters
Therefore, the lengths of each piece are 48 meters, 24 meters, and 12 meters, respectively.