To find the remaining ratio of orange beads for each bracelet, we first need to clarify the ratio that Vie wants for her beads. The given ratio of blue to yellow beads is \(310:110\).
First, we simplify this ratio.
- Find the greatest common divisor (GCD) of 310 and 110. The GCD of these two numbers is 110.
- Divide both numbers by their GCD:
\[ \frac{310}{110} = \frac{310 \div 110}{110 \div 110} = \frac{31}{11} \]
Now, the simplified ratio of blue to yellow beads is \(31:11\).
Next, to find the ratio of orange beads, we can represent the number of orange beads as an additional variable \(x\). However, since we don't have a specific number for orange beads yet, we will denote it in the ratio format:
So, the ratio of blue to yellow to orange can be represented as:
\[ 31:11:x \]
Since we need the entire ratio to be in the simplest form, and we don’t have any specific requirement for the amount of orange beads, we can just denote the ratio of orange beads as \(x\).
Typically, if no specific quantity is indicated for orange beads, it would be expressed in proportion to the other colors. Thus, we can assume that:
\[ x = 1 \]
However, without loss of generality or specific requirements for orange, we can keep the ratio flexible.
Let's express the final relationship as:
\[ 31:11:1 \]
Thus, the simplified ratio of blue to yellow to orange beads is \(31:11:1\).
In summary, the remaining ratio of orange beads for each bracelet is just \(1\) to maintain the structure of the ratio, which can also be expressed as \(x\) indicating the number of orange beads Vie's choice allows for variation.