PSA_PRACTICE_QNR41. Julie Ann has some loom bands to give to her friends.If she gives 6 or 8 loom bands to each friend,she has no left over.If she gives 9 to each friend,she has 3 left ove.Find the smallest number of loom bands Julie Ann can have.
Ans: Let, number of loom bands be 6k1 or 8k2.
We need to find an expression that satisfies both the conditions:
Number pattern for 6k1 : 6, 12, 18, 24, 30, 42, 48, 54, 60, 66, 72….
Number pattern for 8k2 : 8, 16, 24 , 32, 40, 48, 56, 64, 72, …
Observing the common elements, we can observe the series: 24, 48 , 72….
We can write the expression to be 24k.
Also, 24k when divided by 9 gives a remainder 3. Thus, we can write:
24k = 9x + 3 [x is the quotient when 24k is divided by 9].
Rearranging the above equation:
9x = 24k – 3
=> 9x = 18k + (6k -3)
LHS is a multiple of 9. RHS should also be. Since 18k in RHS is already a multiple of 9, (6k -3) should also be.
By trial and error, k=2 makes 6k-3 a multiple of 9. x comes out to be 5.
Thus, the smallest possible number of loom bands = 9x +3 = 48.