Ashort necklace has 32 gold beads and 8 black beads.

a long necklace has a total of 60 beads.

both necklaces have the same ratio of gold beads to black beads.

how many black beads are on the long necklace?

12 black beads

Step-by-step explanation:

Given the ration of gold beads to black beads on the short necklace:

Since the ratio of 4:1 has 5 total parts, you can take the total amount of beads in the long necklace and divide by 5:

60 ÷ 5 = 12

12 beads represents 1 part of the ratio, so that would be the number of black beads.  To check, multiply 12 by 4:  12 x 4 = 48, and set up a ratio:

48: 12 = 4: 1

this is false ^.^ lol