一个盒子里装有一些红球和黄球。起初，红球数量与黄球数量的比是 1 : 3。在拿走 $\frac{1}{4}$ 的红球和 $\frac{3}{8}$ 的黄球后，盒子里还剩 63 个球。请问起初盒子里有多少个黄球？ 答：___

1. Express the initial ratio using a common multiple of denominators to avoid fractions

Initial ratio of Red : Yellow = $1 : 3$.
Fractions taken out are $\frac{1}{4}$ for red and $\frac{3}{8}$ for yellow.
To easily calculate the remaining parts, we can multiply the initial ratio by $8$ (the LCM of $4$ and $8$).
Initial Red : Yellow = $8 : 24$ units.

2. Calculate the remaining units for red and yellow balls

Red balls taken out = $\frac{1}{4} \times 8 = 2$ units.
Red balls left = $8 - 2 = 6$ units.
Yellow balls taken out = $\frac{3}{8} \times 24 = 9$ units.
Yellow balls left = $24 - 9 = 15$ units.
Total units left = $6 + 15 = 21$ units.

3. Find the value of 1 unit and the initial number of yellow balls

$21$ units = $63$ balls
$1$ unit = $63 \div 21 = 3$ balls
Initial yellow balls = $24$ units = $24 \times 3 = 72$ balls.