Anna has 32 red beads, 16 blue beads, and 8 green beads. She wants to put an equal number of each kind of bead on necklaces she is making. How many of each kind of bead can Anna put on each necklace?
Since 16 and 32 are multiples of 8, then
green:blue:red = 8:16:32 = 1:2:4
so, since the divisors of 8 are 1,2,4,8
these are the possible numbers of green beads. Just multiply those by 2 and 4 to get the other colors.
This is good in helping with problem 92
Well, Anna is quite the crafty individual! Now, let's see. To make things equal, we'll have to divide the beads. So, let's gather around and count. If we add up all the beads, we have 32 + 16 + 8, which gives us 56.
Now, since we want an equal number of each kind of bead, we need to divide 56 by 3 (the number of different colors). And guess what? The answer is 18.66666666666666.
Now, I haven't seen a necklace with a fractional bead before, have you? So, Anna might be in a bit of a pickle here. She can't put an equal number of each bead on the necklace considering the whole number situation. But hey, she can definitely distribute as evenly as possible. I suggest she can make necklaces with 18 red, 9 blue, and 4 green beads and save the extra 2 red beads for later. Better safe than sorry, right?
To determine how many of each kind of bead Anna can put on each necklace, we need to find the greatest common divisor (GCD) of the given numbers. The GCD will represent the maximum number of beads that can be evenly divided among the three types.
To find the GCD, we can use the Euclidean algorithm:
1. Start by comparing the largest and smallest numbers (32 and 8 in this case).
- Divide 32 by 8: 32 ÷ 8 = 4.
- The remainder is 0, indicating that 8 is a divisor of 32.
2. Now compare the divisor (8) with the middle number (16).
- Divide 16 by 8: 16 ÷ 8 = 2.
- The remainder is 0, indicating that 8 is a divisor of 16 as well.
3. Since we have no more numbers to compare, the GCD is the divisor in the last step, which is 8.
So, Anna can put 8 of each kind of bead on each necklace.