Aisha had a roll of ribbon. She used \( 15 \% \) of the ribbon to decorate cards and had 17 feet of ribbon left. She then used \( 20 \% \) of the remaining ribbon to wrap gifts. a What was the original length of the roll of ribbon? b What was the remaining length of ribbon after Aisha used them to wrap gifts?

To find the original length of the roll of ribbon, let's denote the original length as \( L \). Since Aisha used \( 15\% \) of the ribbon, that means she had \( 85\% \) left after decorating the cards. According to the problem, this remaining \( 85\% \) equals \( 17 \) feet. So, we can express this as: \[ 0.85L = 17 \] To find \( L \), divide both sides by \( 0.85 \): \[ L = \frac{17}{0.85} = 20 \text{ feet} \] Thus, the original length of the ribbon was \( 20 \) feet. After using \( 15\% \) for decorating cards, Aisha had \( 17 \) feet left. Now she uses \( 20\% \) of this remaining ribbon to wrap gifts. Calculating \( 20\% \): \[ 0.20 \times 17 = 3.4 \text{ feet} \] After wrapping gifts, the remaining length of the ribbon will be: \[ 17 - 3.4 = 13.6 \text{ feet} \] Therefore, after wrapping gifts, Aisha has \( 13.6 \) feet of ribbon left.