\begin{tabular}{l|l|l|} 1.1 In a string of beads, there are two red beads for every five green beads and three \\ purple beads for every 10 green beads. How many purple beads are there in a \\ string with 12 red beads? \\ A. 50 \\ B. 10 \\ C. 9 & 9 \\ D. 15 \\ E. 18 & \\ \hline\end{tabular}

To find the number of purple beads in a string with 12 red beads, let's first establish the ratios given in the problem. The ratio of red beads to green beads is 2:5. If there are 12 red beads, we can use the ratio to find the number of green beads: \[ \text{Green beads} = \frac{5}{2} \times \text{Red beads} \] \[ \text{Green beads} = \frac{5}{2} \times 12 = 30 \] Now, for the purple beads, the ratio of purple beads to green beads is 3:10. So, we can calculate the number of purple beads as follows: \[ \text{Purple beads} = \frac{3}{10} \times \text{Green beads} \] \[ \text{Purple beads} = \frac{3}{10} \times 30 = 9 \] Thus, the number of purple beads in a string with 12 red beads is **9** (option C). If you're curious, this problem is a classic example of using ratios to solve for unknowns, a method that’s handy in various real-life situations, like determining ingredients for recipes or calculating materials for crafts! Want to dive deeper? There are loads of fun resources on ratios and proportions available online, from interactive quizzes to engaging video lessons that can expand your understanding in a more laid-back way!