I never know how to make a double matrix solution look neat in the plaintext format of these posts, so I prepared a full solution in the pdf attached.
The double matrix method is a powerful method for solving problems like this. In Magoosh, among our over 100 Math Lesson Videos, we have one that demonstrates exactly how to use the double matrix method. See https://gmat.magoosh.com/plans for details.
Here's a free question along the same lines:
https://gmat.magoosh.com/admin/questions/21
Once you enter a solution to the question at that link, it should be followed by a video that gives a complete explanation.
I hope this helps. Let me know if you have any further questions.
Mike
