Answer
1285 messages
Work Step by Step
The cost of the bill is:
$C=10+0.1(m-1000)$, where $m$= number of messages, assuming the person has sent over 1000 messages that month.
For Miriam, we have:
$38.50=10+0.1(m-1000)$
We solve for $m$:
$m=1000+(38.50-10)/0.1=1000+285=1285$
Thus she sent $1285$ messages in June.