Three girls used the same number of small pebbles to make necklaces. Irene used ³₅ of her small pebbles, Nora used ⁴₅ of hers and Xandra used ²₃ of hers. They had a total of 106 small pebbles at first. How many small pebbles did each girl use?
Make the numerators the same.   

LCM of 3, 4 and 2 = 12

³₅ Irene's small pebbles = ⁴₅ Nora's small pebbles = ²₃ Xandra's small pebbles
^3x4_5x4 Irene's small pebbles = ^4x3_5x3 Nora's small pebbles = ^2x6_3x6 Xandra's small pebbles
¹²₂₀ Irene's small pebbles = ¹²₁₅ Nora's small pebbles = ¹²₁₈ Xandra's small pebbles

	Irene	Nora	Xandra
Before	20 u	15 u	18 u
Change	- 12 u	- 12 u	- 12 u
After	8 u	3 u	6 u

Total number of small pebbles at first
= 20 u + 15 u + 18 u
= 53 u

53 u = 106

1 u = 106 ÷ 53 = 2

Number of small pebbles that each girl used
= 12 u
= 12 x 2
= 24

Answer(s): 24