fewest number

Question

Diana has a bag of beads. When asked how many beads are in the bag, she said. I can make sets of 2 beads, 4 beads and 5 beads and not have any left over. when I divide the beads into 9 sets I have 7 left over.  what is the fewest number of beads Diana can have?

Answer 1

If you can make sets of 2 beads, sets of 4 beads, and sets of 5 beads, and not have any left over, you want the least common multiple of 2,4, and5 which is 20. You can write multiples of 20 until you get the correct answer.

20/9=2 R2

40/9=4 R4

60/9=6 R6

80/9=8 R8

100/9=11 R1

120/9=13 R3

140/9=15 R5

160/9=17 R7 answer

160 is the smallest multiple of 20 such that when you divide it by 9 you have 7 as a remainder

160 is the fewest number of beads whereby you can make sets of 2, 4, and 5 but when you make sets of 9 you get 17 sets and 7 beads remaining

 

a simpler approach is to multiply 20 by 9 to get 180, but 180 is divisible by 9 with no remainder

now work backwards and use the multiple 160 and as you have seen 160/9=17 R7

you also should see a pattern of remainders with the first solution:

remainder 2, then 4, then 6, 8, 1, 3, 5, and finally 7