Final answer:
Kyle's glass mosaic uses a width to length ratio of 1 1/4 inches to 2 1/2 inches. The calculated unit rate is 0.5, meaning the width of the pieces is 1.25 inches, and the length is 2.5 inches. The correct statements are that the width of each piece is 1.25 inches (C) and the length is 2.5 inches (D).
Step-by-step explanation:
Kyle is working on a glass mosaic and wants to maintain a width to length ratio of 1 1/4 inches to 2 1/2 inches for each piece. We need to calculate the unit rate of the pieces to determine the truth of the given statements.
Firstly, to find the unit rate, we need to convert the ratio to improper fractions and then divide:
Width = 1 1/4 = 5/4 inches
Length = 2 1/2 = 5/2 inches
Unit rate (width to length) = (5/4) ÷ (5/2) = (5/4) × (2/5) = 10/20 = 1/2
Thus, the unit rate is 0.5, which corresponds to a half-inch of width for every inch of length.
Using the unit rate to check the statements given:
- A) The width of each piece is 2 inches. False
- B) The length of each piece is 3 inches. False
- C) The width of each piece is 1.25 inches. True (because 1.25 inches is 5/4 inches)
- D) The length of each piece is 2.5 inches. True (because 2.5 inches is 5/2 inches)
- E) The unit rate is 0.5. True
Therefore, the correct statements are C and D: The width of each piece is 1.25 inches, and the length of each piece is 2.5 inches.