Robin has 7 red beads, 27 purple beads, and 24 yellow beads. She wants to make a necklace with the pattern; red bead; 3 purple beads; 2 yellow beads. How many times can she repeat the pattern? Which color of beads will she run out of first?
each cycle uses 6 beads, in the ratio 1:3:2 =
7:21:14
You can see that 7 cycles will use up all the reds, with others left over.
To determine how many times Robin can repeat the pattern, we need to find the limiting factor—the color of beads that she runs out of first.
First, let's look at the pattern: red bead, 3 purple beads, 2 yellow beads. This consists of 1 red bead, 3 purple beads (3 x 1 = 3 purple beads), and 2 yellow beads (2 x 1 = 2 yellow beads). Therefore, each repetition of the pattern requires a total of 1 red bead, 3 purple beads, and 2 yellow beads.
Now, let's compare the number of beads Robin has with the amount required for each repetition:
- Red beads: Robin has 7 red beads, and each repetition requires 1 red bead. So, she can repeat the pattern 7 times.
- Purple beads: Robin has 27 purple beads, and each repetition requires 3 purple beads. To find out how many times she can repeat the pattern, we divide the number of purple beads by 3: 27 ÷ 3 = 9. Therefore, she can repeat the pattern 9 times.
- Yellow beads: Robin has 24 yellow beads, and each repetition requires 2 yellow beads. To find out how many times she can repeat the pattern, we divide the number of yellow beads by 2: 24 ÷ 2 = 12. So, she can repeat the pattern 12 times.
Since Robin can repeat the pattern the fewest number of times using the red beads (7 times), it means she will run out of red beads first.
Therefore, Robin can repeat the pattern 7 times, and she will run out of red beads first.