Latrice and Meagan are collecting coins. Latrice doubled her coin collection the first month, and then added 200 coins to her collection the second month. Meagan added 85 coins to her collection the first week, and then doubled her total the second week. Now Latrice and Meagan have the same number of coins. The equation below can be used to find out when both companies charge the same amount.

2x+ 200 = 2(x + 85)

Is there any number of text messages that will result in the exact same charge from both companies? If yes, what number works? If no, explain why not.