Certainly! Let's solve the problem step by step.
1. Understand the ratio:
The ratio of pink marbles to purple marbles is [tex]\( \frac{1}{3} \)[/tex]. This means for every 1 pink marble, there are 3 purple marbles.
2. Identify the number of pink marbles:
We are given that the number of pink marbles in the bag is 3.
3. Calculate the number of purple marbles:
According to the ratio [tex]\(1:3\)[/tex], for every 1 pink marble, there are 3 purple marbles.
Given the number of pink marbles is 3, we can find the number of purple marbles by multiplying the number of pink marbles by the ratio of purple marbles to pink marbles.
[tex]\[
\text{Number of purple marbles} = 3 \times 3 = 9
\][/tex]
4. Calculate the total number of marbles:
We now know the number of pink marbles and purple marbles.
[tex]\[
\text{Total number of marbles} = \text{Number of pink marbles} + \text{Number of purple marbles}
\][/tex]
Substituting in the values:
[tex]\[
\text{Total number of marbles} = 3 + 9 = 12
\][/tex]
5. Summarize the solution:
- Number of pink marbles [tex]\(= 3\)[/tex]
- Number of purple marbles [tex]\(= 9\)[/tex]
- Total number of marbles [tex]\(= 12\)[/tex]
So, if there are 3 pink marbles in the bag, the number of purple marbles is 9 and the total number of marbles in the bag is 12.
