珍妮特、塞缪尔和法哈娜制作一些冰棒时使用了相同数量的冰棒棍。珍妮特剩下了她所有冰棒棍的 $\frac{3}{7}$。塞缪尔剩下了他所有冰棒棍的 $\frac{1}{4}$。法哈娜剩下了她所有冰棒棍的 $\frac{7}{9}$。他们一共剩下 1265 根冰棒棍。他们每人制作冰棒使用了多少根冰棒棍？ 答: ___

1. Find the fraction of ice-cream sticks used by each person.

Fraction used by Janet = $1 - \frac{3}{7} = \frac{4}{7}$
Fraction used by Samuel = $1 - \frac{1}{4} = \frac{3}{4}$
Fraction used by Farhana = $1 - \frac{7}{9} = \frac{2}{9}$

2. Make the numerators of the fractions used the same, since they used the same number of sticks.

The numerators are $4$, $3$, and $2$. The lowest common multiple is $12$.
Janet used: $\frac{4}{7} = \frac{12}{21}$
Samuel used: $\frac{3}{4} = \frac{12}{16}$
Farhana used: $\frac{2}{9} = \frac{12}{54}$

3. Find the number of units left for each person and the total units left.

Units left for Janet = $21 - 12 = 9$
Units left for Samuel = $16 - 12 = 4$
Units left for Farhana = $54 - 12 = 42$
Total units left = $9 + 4 + 42 = 55$ units

4. Calculate the value of 1 unit and the number of sticks used by each person.

$55 \text{ units} = 1265$
$1 \text{ unit} = 1265 \div 55 = 23$
Number of sticks used by each person = $12 \text{ units} = 12 \times 23 = 276$