Dawn and Emily each had the same length of ribbon. Both girls used their ribbons to make identical bows. Dawn made 12 bows and had 128 cm of ribbon left. Emily made 9 bows and had 176 cm of ribbon left. How many bows could Emily make with the ribbon she had left?

This problem involves Dawn and Emily, who each started with the same length of ribbon. They used their ribbons to make bows, but each girl made a different number of bows and had different amounts of ribbon left. The goal is to find out how many bows Emily could have made with the ribbon she had left, given the amounts she used for her bows.

Explanation:

Let the total length of the ribbon each girl started with be denoted as $L$ (in cm).

We know:

• Dawn made 12 bows and had 128 cm of ribbon left.

• Emily made 9 bows and had 176 cm of ribbon left.

For each girl, the total amount of ribbon used to make the bows can be expressed as:

• Ribbon used by Dawn: $12 \times \text{length of each bow}$ + 128 cm (leftover).

• Ribbon used by Emily: $9 \times \text{length of each bow}$ + 176 cm (leftover).

Since both girls started with the same length of ribbon, we can set up an equation to find the length of ribbon used for each bow.

Let’s represent the length of each bow as $x$ cm. Then:

• The total length of ribbon Dawn started with is $12x + 128$.

• The total length of ribbon Emily started with is $9x + 176$.

Since the total lengths of ribbon are the same, we can equate the two expressions:

$$12x + 128 = 9x + 176$$

Now, we solve for $x$ to find the length of each bow.

Solution:

1. Start with the equation:

$$12x+128=9x+176$$

2. Subtract $9x$ from both sides:

$$3x+128=176$$

3. Subtract 128 from both sides:

$$3x=48$$

4. Divide both sides by 3:

$$x=16$$

So, each bow is 16 cm long.

Now, let’s find how many bows Emily could have made with the ribbon she had left (176 cm).

Since each bow is 16 cm long, the number of bows Emily could make with her leftover ribbon is:

$$\frac{176}{16} = 11$$

Answer:

Emily could have made 11 bows with the ribbon she had left.

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