Sydney wants to make 15 beaded rings for a craft show. She needs 60 beads for each ring. She has 852 beads. Does Sydney have enough beads to make 15 complete rings?

To determine if Sydney has enough beads to make 15 complete rings, we need to calculate the total number of beads she will need for all 15 rings and then compare that to the number of beads she currently has.

1. Calculate the total number of beads needed for 15 rings: Each ring requires 60 beads. Therefore, for 15 rings, the total number of beads needed can be calculated as follows:

   \[ \text{Total beads needed} = \text{Number of rings} \times \text{Beads per ring} \] \[ \text{Total beads needed} = 15 \times 60 \] \[ \text{Total beads needed} = 900 \]

2. Compare the total beads needed with the beads Sydney has: Sydney has 852 beads. Now we will see if 852 beads are enough to meet the requirement of 900 beads:

   \[ \text{Beads Sydney has} = 852 \] \[ \text{Beads needed} = 900 \]

   Since 852 is less than 900, we evaluate:

   \[ 852 < 900 \]

3. Conclusion: Since Sydney needs 900 beads to make 15 complete rings but only has 852 beads, she does not have enough beads. She is short by:

   \[ \text{Shortage} = 900 - 852 = 48 \]

In summary, Sydney does not have enough beads to make 15 complete rings; she is short by 48 beads.