Hi this question is in the 'GCSE Mathematics for AQA Higher Student Book' that we use at school
I am getting confused with the second simultaneous equation they have derived here as I believe it should be 2w=r . Which one is correct?
Also, working out my simultaneous equation I obtained that the number of white roses is 10 and the number of red roses is 20 which would agree with the original statement that there are twice as many red rose bushes as white, right? However, the book has the complete opposite answers to me with r=10 and w=20 , surely the book is wrong? Thank you.

Yes, the way it is worded you should get $2w=r$ and your solution is correct.