A friend of yours came out of the post office after spending $14 on 15 cent, 20 cent, and 35 cent stamps. If she bought 45 stamps in all, how many of each type did she buy?

the answer is 15 cent stamps = 3t 100, 20 cent stamps = 145 4t, 35 cent stamps = t, where t = 34, 35, 36

Please help me to solve it and explain