It takes 56 colored beads to make a necklace. The beads are strung in the following order: one blue, two yellow, two green, and one red. Then the pattern repeats, starting again with the one blue bead. If the first bead is blue, what is the color of the last bead used? Show your work!
Thank you
yellow
yellow is correct, i just repeated the pattern until i got to 56
blue yellow yellow green green red blue yellow yellow green green red
blue yellow yellow green green red
blue yellow yellow green green red
blue yellow yellow green green red
blue yellow yellow green green red
blue yellow yellow green green red
blue yellow yellow green green red
blue yellow yellow green green red
blue yellow!
GCF MATH
To find the color of the last bead used, we need to determine the pattern of colors that repeats in the necklace.
The given pattern is: one blue, two yellow, two green, and one red. This pattern consists of 6 beads in total.
Since the necklace is made up of 56 beads, we need to find out how many times this pattern can be repeated within 56 beads.
To do that, we divide 56 by 6 (the number of beads in the pattern):
56 / 6 = 9 with a remainder of 2
This means that the pattern can be repeated 9 times with 2 extra beads.
Now, let's determine the color of the last bead used:
Starting with the first blue bead, we can count the number of beads until we reach the last bead.
In each repetition of the pattern, there are 6 beads:
- One blue
- Two yellow
- Two green
- One red
Since we have 9 repetitions of the pattern, the first 54 beads will consist of the entire pattern repeated 9 times (9 x 6 = 54).
This means that we have used up all the beads in the pattern, and there are 2 extra beads remaining.
Counting from the last bead of the pattern (one red), we can determine the color of the remaining beads:
- Two extra beads:
- The 55th bead would be blue
- The 56th bead would be yellow
Therefore, the color of the last bead used in the necklace, if the first bead is blue, is yellow.
So the answer is: The last bead used is yellow.