You can send up to 66 text messages.
Work Step by Step
Let t be the number of text messages you can send. The cost of the text messages is \$0.15 each, or $0.15t$. If you can spend no more than \$10, the cost of the text messages must be less than or equal to \$10. $0.15t\leq10\longrightarrow$ divide each side by 0.15 $0.15t\div0.15\leq10\div0.15$ $t\leq66.\overline6$ Since it is not possible to send a fraction of a text message and rounding up would make the cost exceed \$10, $t\leq66$