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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?

Ask by Robbins Bob. in the United States
Jan 22,2025

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Answer

a. The original length of the ribbon was **20 feet**. b. After wrapping gifts, **13.6 feet** of ribbon remained.

Solution

Let's solve the problem step by step. ### Part a: Finding the Original Length of the Ribbon Let \( L \) be the original length of the ribbon. 1. **Usage for Decorating Cards:** - Aisha used \( 15\% \) of the ribbon to decorate cards. - Therefore, the remaining ribbon after this usage is \( 85\% \) of \( L \). \[ 0.85L = 17 \text{ feet} \] 2. **Solving for \( L \):** \[ L = \frac{17 \text{ feet}}{0.85} = 20 \text{ feet} \] **Answer:** The original length of the ribbon was **20 feet**. ### Part b: Calculating the Remaining Ribbon After Wrapping Gifts After decorating the cards, Aisha had **17 feet** of ribbon left. 1. **Usage for Wrapping Gifts:** - She used \( 20\% \) of the remaining ribbon to wrap gifts. - The length of ribbon used for gifts is: \[ 0.20 \times 17 \text{ feet} = 3.4 \text{ feet} \] 2. **Calculating Remaining Ribbon:** \[ 17 \text{ feet} - 3.4 \text{ feet} = 13.6 \text{ feet} \] **Answer:** After wrapping gifts, **13.6 feet** of ribbon remained. ### Summary a. **20 feet** b. **13.6 feet**

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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.

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