Question: 15. Sumita and Carrie each had a ribbon of same length. Sumita used 75.6 cm of her ribbon to decorate some presents and Carrie used 46.8 cm of her ribbon to make bows. After using the ribbons, Carrie had 4 times as much ribbon left as Sumita. What was the original length of their ribbon?
1. **State the problem:** Sumita and Carrie start with ribbons of the same length $x$ cm.
2. Sumita used $75.6$ cm, so she has $x - 75.6$ cm left.
3. Carrie used $46.8$ cm, so she has $x - 46.8$ cm left.
4. Carrie has 4 times as much ribbon left as Sumita:
$$x - 46.8 = 4(x - 75.6)$$
5. Expand the right side:
$$x - 46.8 = 4x - 302.4$$
6. Rearrange to isolate $x$:
$$x - 4x = -302.4 + 46.8$$
$$\cancel{x} - 4\cancel{x} = -302.4 + 46.8$$
$$-3x = -255.6$$
7. Divide both sides by $-3$:
$$\frac{-3x}{-3} = \frac{-255.6}{-3}$$
$$x = 85.2$$
8. **Answer:** The original length of each ribbon was $85.2$ cm.