mary has 108 red beads and 90 green beads she wants to use all the beads. how many necklaces can she make and how many of each color will be on each necklace
How many beads on each necklace?
i said 9 necklaces and 10 and 12 of each color???
Right.
To find out how many necklaces Mary can make and how many of each color will be on each necklace, we need to consider the total number of beads and find the greatest common divisor (GCD) of the number of red and green beads.
First, we find the GCD of 108 and 90. To do this, we can use the Euclidean algorithm:
Step 1: Divide 108 by 90. The remainder is 18.
Step 2: Divide 90 by 18. The remainder is 0.
Since the remainder is 0, we can conclude that the GCD of 108 and 90 is 18.
The GCD represents the number of beads that should be on each necklace. Therefore, Mary can make 18 necklaces, and each necklace will have 18 beads. To determine how many beads of each color will be on each necklace, we divide the total number of beads of each color by the GCD:
Number of red beads on each necklace = 108 ÷ 18 = 6
Number of green beads on each necklace = 90 ÷ 18 = 5
Therefore, Mary can make 18 necklaces, and each necklace will have 6 red beads and 5 green beads.