Ian and his children went into a bakery where they sell donuts for $1.50 each and cookies for $0.75 each. Ian has $15 to spend and must buy at least 13 donuts and cookies altogether. If Ian decided to buy 4 donuts, determine the maximum number of cookies that he could buy.
Ian has to pay $1.50 x 4 = $<<1.5*4=6>>6 for buying the 4 donuts.
So, he has $15 - $6 = $<<15-6=9>>9 left to buy the cookies.
And, the maximum number of cookies he can buy is $9/$0.75 = <<9/0.75=12>>12 cookies. Answer: \boxed{12}.