A bracelet is made of yellow, green, blue, purple and red beads in that order. the first bead is yellow, and the last bead is blue for each color. what is the maximum number of beads that are in the bracelet if it contains fewer than 90 beads.
the beads recur in cycles of 5 colors.
85 is the largest multiple of 5 which is less than 90. So bead #85 is red.
After that is yellow,blue, making 87 beads in all.
I have no idea what "the first bead is yellow, and the last bead is blue for each color" means, since you already gave the order of the colors.
If I have it wrong, follow my logic and get it right.
To determine the maximum number of beads in the bracelet, we need to find the maximum number of beads for each color and sum them together.
We know the order of the colors is yellow, green, blue, purple, and red. Let's assume the number of beads per color is represented by the variables y, g, b, p, and r, respectively. Since the first bead is yellow and the last bead is blue, we know that both y and b must be odd numbers (since the total number of beads is an odd number).
Now, let's determine the maximum value for each variable and add them together to find the maximum number of beads:
y (yellow): We know y must be an odd number, and since it is the first bead, we can assume it to be 1.
g (green): The maximum number of green beads would be when there are the same number of green beads as yellow beads. Since y = 1, the maximum value for g is also 1.
b (blue): We know b must be an odd number since it is the last bead. The maximum value for b will be the maximum value for y, which is 1.
p (purple): The maximum number of purple beads would be when there are the same number of purple beads as green beads. Since g = 1, the maximum value for p is also 1.
r (red): Since the total number of beads is an odd number, the remaining beads after yellow, green, blue, and purple will all be red. Therefore, the maximum value for r would be (total number of beads - (y + g + b + p)).
Now let's calculate the maximum number of beads:
Maximum number of beads = y + g + b + p + r
= 1 + 1 + 1 + 1 + (total number of beads - (1 + 1 + 1 + 1))
= 4 + (total number of beads - 4)
= total number of beads
So, the maximum number of beads in the bracelet is equal to the total number of beads.
Since the question states that there are fewer than 90 beads, the maximum number of beads in the bracelet is 89.