On the sign is a 4 digit number. You need to use the digits of this number to calculate the coordinates of the final stage. Call these digits ABCD.
Subtract the first digit from the whole number of the minutes in the North latitude at the first location. (15-A). This will give you the whole number of the North minutes at the final location.
Add the third digit to the whole number of the minutes in the West longitude (38+C). This will give you the whole number of the West minutes at the final location.
Multiply the second number by 3. Taking the decimal portion of the minutes of the North latitude at the first location as a whole number, subtract the product to get the decimal portion of the North minutes at the final location. (31-3B) Note: you will have to put the zeroes back into the decimal because you are using .031 as just 31, so if your answer is 8 you will have to look for .008. (If your answer is 8, it is wrong.)
OK so far? The last one is more complicated. Multiply the first number by 3; multiply the second number by 20; multiply the third number by 5 and multiply the fourth number by 30. Again taking the decimal portion of the Minutes as a whole number, subtract each of the four products from the decimal portion of the Minutes of the West longitude at the first location to get the decimal portion of the Minutes at the final location. (640-3A-20B-5C-30D)
Now go find the cache.