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?
Each had L cm of ribbon.
Dawn: (L-128)cm/12Bows = cm/Bow.
Emily: (L-176)cm/9Bows = cm/Bow.
Since the bows were equal, each used the same cm/bow:
(L-128)/12 = (L-176)/9.
L = 320 cm of ribbon for each girl.
Emily: (320-176)/9 = 16cm/Bow.
176cm/(16cm/bow) = 11 Bows she can make with ribbon left.
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To find out how many bows Emily could make with the ribbon she had left, we need to determine the length of the ribbon they started with. Since Dawn made 12 bows and had 128 cm left, we can calculate how much ribbon she used for the 12 bows by subtracting the amount she had left from her initial ribbon length.
Dawn's initial ribbon length = Ribbon used for bows + Ribbon left
Let's say her initial ribbon length is "x" cm.
So, x - 128 cm = Ribbon used for 12 bows
Similarly, Emily's initial ribbon length can be determined by subtracting the amount she had left from her ribbon length after making 9 bows.
Emily's initial ribbon length = Ribbon used for bows + Ribbon left
Let's say her initial ribbon length is "y" cm.
So, y - 176 cm = Ribbon used for 9 bows
Now, since Dawn and Emily started with the same length of ribbon, we can equate their initial ribbon lengths:
x = y
We can set up the following equation by substituting the values we found earlier:
x - 128 cm = Ribbon used for 12 bows
y - 176 cm = Ribbon used for 9 bows
Since they both used the same amount of ribbon for the identical bows, we can equate the ribbon used for 12 bows with the ribbon used for 9 bows:
x - 128 cm = y - 176 cm
Simplifying the equation:
x - y = 176 cm - 128 cm
x - y = 48 cm
Since x = y, we can rewrite the equation as:
x - x = 48 cm
0 = 48 cm
As we can see, this equation does not have a valid solution. It seems there is an error in the given information or the question itself.
Let b = the length of ribbon both people originally had.
Let c = the length of ribbon it takes them to make one bow
Then, the question statest that:
b = 12 * c + 128
and
b = 9 * c + 176
Let's substitute b from the first equation into the second equation (system of equations). Then, we get:
12 * c + 128 = 9 * c + 176
3 * c + 128 = 176 <- Subtract 9*c both side
3 * c = 48 <- Subtrac 128 from both sides
c = 16 <- Divide both sides by 3
So this means that it takes 16 cm of ribbon to create one bow. Since Emily has 176 cm of ribbon left, she can create:
176/3 (rounded down) more bows.
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?
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