Quantity of Beads Price 100 beads $6.00 200 beads $10.00 400 beads $16.00 600 beads $30.00 1000 beads $55.00 Kayla uses fancy beads which she purchases online to make bangle bracelets. The chart shows the number of different designer beads in one bag, and only full bags are sold. If Kayla chooses the BEST DEAL, how much will 1200 beads cost? A) $48.00 B) $56.00 C) $65.00 D) $70.00
Answers
Step-by-step explanation:
I'm going to call the length of the bracelet the number of times you have to add to get back to the first bead. This is the same as the number of beads, except in one case:
The shortest bracelet has length 1 and starts with (0,0). If you add one time, you get back to the first 0. But the bracelet has two beads. (Every bracelet has to have at least two beads to start.)
The next shortest bracelet starts with (0,5), and has length 3:
0 5 5
There is a bracelet of length 4 that starts with (2,6) (the first example on the main page):
2 6 8 4
There is a bracelet of length 12 that starts with (1,3) (the second example on the main page):
1 3 4 7 1 8 9 7 6 3 9 2
There is a bracelet of length 20 that starts with (0,4)
0 4 4 8 2 0 2 2 4 6 0 6 6 2 8 0 8 8 6 4
There is a bracelet of length 60 that starts with (0,1)
(I'll let you have the fun of writing all the beads.)
How many different starting pairs of beads are there?
There are 10 choices for the first bead:
0 1 2 3 4 5 6 7 8 9
For each of these choices there are the same 10 choices for the second bead. For example, if the first bead is 0, the possibilities for the first two beads are
(0,0) (0,1) (0,2) (0,3) (0,4) (0,5) (0,6) (0,7) (0,8) (0,9) [10 choices]
So there are 10 x 10 = 100 pairs in all.
The order of the numbers is important, so we have to count ordered pairs: pairs of numbers in a particular order. In mathematics, ordered pairs are written in parentheses with a comma in between: (2,6)