Ice cream cones are sold by a vendor for $\$ 1.25$ each. The vendor pays $\$ 250$ per month to rent his booth. What is his profit for a month in which he sells 3,200 ice cream cones and spends $\$ 2,947.28$ on supplies?

Step 1 ：Let's denote the price per cone as \(P\), the rent as \(R\), the cost of supplies as \(S\), and the number of cones sold as \(N\). Given that \(P = \$1.25\), \(R = \$250\), \(S = \$2947.28\), and \(N = 3200\).

Step 2 ：The total income, \(I\), is calculated by multiplying the number of cones sold by the price per cone. So, \(I = P \times N = \$1.25 \times 3200 = \$4000\).

Step 3 ：The total expenses, \(E\), is the sum of the rent and the cost of supplies. So, \(E = R + S = \$250 + \$2947.28 = \$3197.28\).

Step 4 ：The profit, \(\Pi\), is calculated by subtracting the total expenses from the total income. So, \(\Pi = I - E = \$4000 - \$3197.28 = \$802.72\).

Step 5 ：\(\boxed{\text{Final Answer: The vendor's profit for the month is approximately \$802.72.}}\)