Lopez spent 1/3 of his vacation money for travel in 2/5 of his vacation money for lodging. he spent $1,100 for travel and lodging what is the total amount of money he spent on his vacation

The answer is $2,062.50
$1,100=1/3 + 1/5 of his money
therefore 1,100 = 5/15 + 3/15 = 8/15
I want to know what 15/15 is equal to
therefore I must first determine 1/15
1,100/8 = 137 1/2 = 1/15
The entire sum of money is 15/15 so it is 137 1/2 * 15 = $2,062.50