Answer:

The initial costs of the two pairs of shoes were $246 and $410.

Step-by-step explanation:

Let the initial costs of the two pairs of shoes be 3x and 5x, where x is a constant. Then, we can write:

New cost of the first pair of shoes = 3x + 200

New cost of the second pair of shoes = 5x + 200

According to the problem, the ratio of the new costs is 13:20, so we can write:

(3x + 200)/(5x + 200) = 13/20

Cross-multiplying and simplifying, we get:

60(3x + 200) = 13(5x + 200)

180x + 12000 = 65x + 2600

115x = 9400

x = 82

Therefore, the initial costs of the two pairs of shoes were:

First pair: 3x = 3(82) = 246

Second pair: 5x = 5(82) = 410

So the initial costs of the two pairs of shoes were $246 and $410.