Answer :
Evan could make 16 bows with the ribbon he had left.
Let's denote the length of the ribbon Julia and Evan each had as "R" centimeters.
Julia made 12 bows and had 128 centimeters of ribbon left, so she used R - 128 centimeters for the 12 bows. Therefore, the length of ribbon required to make one bow for Julia is (R - 128) / 12 centimeters.
Evan made 9 bows and had 176 centimeters of ribbon left. So, he used R - 176 centimeters for the 9 bows. Therefore, the length of ribbon required to make one bow for Evan is (R - 176) / 9 centimeters.
Since they used the same length of ribbon to make identical bows, we can set these two expressions equal to each other:
(R - 128) / 12 = (R - 176) / 9
Now, we can solve for R:
9(R - 128) = 12(R - 176)
9R - 1152 = 12R - 2112
Subtract 9R from both sides:
-1152 = 3R - 2112
Now, add 2112 to both sides:
3R = 960
Finally, divide by 3:
R = 320
So, the original length of the ribbon Julia and Evan each had was 320 centimeters.
Now that we know the original length, we can calculate how many bows Evan could make with the ribbon he had left:
Evan had 176 centimeters of ribbon left, and each bow requires (320 - 176) / 9 centimeters of ribbon:
(320 - 176) / 9 = 144 / 9 = 16
Evan could make 16 bows with the ribbon he had left.
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