Let's assume the number of roses in each arrangement is represented by "r".
Since Vanessa makes 7 identical flower arrangements, the total number of roses used in all the arrangements is 7r.
We know that each arrangement contains 9 tulips, so the total number of tulips used in all the arrangements is 7 * 9 = 63.
The total number of flowers used in all the arrangements is given as 147.
Therefore, we can write the equation:
7r + 63 = 147
To find the number of roses (r), we can solve this equation.
Subtracting 63 from both sides of the equation:
7r = 147 - 63
7r = 84
Dividing both sides of the equation by 7:
r = 84 / 7
r = 12
Hence, there are 12 roses in each flower arrangement.