[tex] \\ \text{Let the number of each type stamps bought are x.}\\ \\ \text{so the amount paid to buy 14 cents stamps }=0.14 x\\ \\ \text{and the amount paid to buy the stamps costing 22 cents is}=0.22 x\\ \\ \text{now since he paid a total of }\$1.80 \text{ for all the stamps, }\\ \text{so we have}\\ \\ 0.14x+0.22 x=1.80\\ \\ \Rightarrow 0.36x=1.80\\ \\ \Rightarrow x=\frac{1.80}{0.36}\\ \\ \Rightarrow x=5 [/tex]
Hence Felipe Vasquez bought 5 stamps of each kind.