Final answer:
Michele needs 20 blue beads to maintain a 3:2 ratio of yellow to blue beads for her key chains, calculated by setting up a proportion based on the number of yellow beads she has.
Step-by-step explanation:
To find out how many blue beads Michele needs to accompany her 30 yellow beads to make key chains with a ratio of 3 yellow beads for every 2 blue beads, we need to set up a proportion. Michele wants a 3:2 ratio of yellow to blue beads. If Y represents the number of yellow beads and B represents the number of blue beads, then Y/B = 3/2.
Since Michele has 30 yellow beads (Y = 30), we can plug this number into the proportion 30/B = 3/2. To find the value of B (the number of blue beads needed), we cross-multiply and get 2 × 30 = 3 × B, which simplifies to 60 = 3B.
Dividing both sides of the equation by 3 yields B = 60/3, which gives us B = 20. Therefore, Michele needs 20 blue beads to maintain the desired color ratio of 3:2 for her key chains.