Down and Emily each had the same length of ribbon. Both girls used their ribbons to make identical bows. Down made 12 bows and had 128 cm of ribbon left. Emily made 0 bows and had 176 cm of ribbon left. How many bows could Emily make with the ribbon she had left?
Down and Emily each had the same length of ribbon. Both girls used their ribbons to make identical bows. Down made 12 bows and had 128 cm of ribbon left. Emily made 0 bows and had 176 cm of ribbon left. How many bows could Emily make with the ribbon she had left?
The Correct Answer and Explanation is:
To solve the problem, let’s define the unknowns:
Let x be the total length of ribbon each girl originally had.
Let b be the length of ribbon required to make one bow.
From the problem:
- Down made 12 bows and had 128 cm of ribbon left.
So, the ribbon used for 12 bows is 12b12b, and she had 128 cm remaining.
That gives the equation: x=12b+128(1)x = 12b + 128 \quad \text{(1)} - Emily made 0 bows and had 176 cm of ribbon left.
So, all of her ribbon is still available: x=176(2)x = 176 \quad \text{(2)}
Now substitute equation (2) into equation (1): 176=12b+128176 = 12b + 128
Subtract 128 from both sides: 176−128=12b48=12b176 – 128 = 12b \\ 48 = 12b
Solve for b: b=4812=4b = \frac{48}{12} = 4
So, each bow requires 4 cm of ribbon.
Now, to find how many bows Emily can make with her 176 cm of ribbon: Number of bows=1764=44\text{Number of bows} = \frac{176}{4} = 44
✅ Final Answer: Emily can make 44 bows.
📘 Explanation
This problem is a classic example of using algebra to determine how many units of a product can be made from a limited resource. Both Down and Emily started with the same amount of ribbon. Down used part of her ribbon to make bows and had 128 cm left, while Emily didn’t make any bows and had the full 176 cm remaining. This tells us that 176 cm was the original ribbon length for both.
Down used ribbon to make 12 bows. That means the difference between 176 cm and 128 cm (which is 48 cm) was used for those 12 bows. By dividing 48 cm by 12 bows, we calculate that each bow uses 4 cm of ribbon.
With this information, we can now determine how many bows Emily could make using her 176 cm of ribbon. If each bow requires 4 cm, then dividing 176 by 4 gives 44 bows.
This problem showcases how to:
- Translate real-world situations into equations,
- Use substitution to solve for unknowns,
- Interpret and apply the result logically.
It also reinforces the importance of understanding units (like centimeters and number of bows) and how they relate. The key insight was recognizing that Emily’s full ribbon (176 cm) equals the amount Down had before making any bows, allowing us to isolate the cost of each bow and compute the total number Emily could make.
Thus, Emily can make 44 identical bows with her ribbon.
