lopez spent 1/3 of his vacation money for travel and 2/5 of his vacation money for lodging. He spent $1100 for travel and lodging. What is the total amount of money he spent on his vacation?
To find the total amount of money Lopez spent on his vacation, we need to determine the fraction of his vacation money he spent for travel and lodging separately, and then calculate the total amount.
Let's assign a variable to represent the total amount of money Lopez had for his vacation. Let's call it "T".
According to the problem, he spent 1/3 of his vacation money on travel and 2/5 of his vacation money on lodging.
So, the amount of money he spent on travel can be found by multiplying the fraction spent on travel (1/3) by the total amount of money he had for vacation (T):
Amount spent on travel = (1/3) * T
Similarly, the amount of money he spent on lodging can be found by multiplying the fraction spent on lodging (2/5) by the total amount of money he had for vacation (T):
Amount spent on lodging = (2/5) * T
We are given that he spent a total of $1100 for travel and lodging. So, we can set up the following equation:
Amount spent on travel + Amount spent on lodging = $1100
(1/3) * T + (2/5) * T = $1100
Now, we can solve this equation to find the value of T, which represents the total amount of money he had for vacation.
1/3 + 2/5 = 5/15 + 6/15 = 11/15
is the fraction of total vacation expenses (V) that is for travel and lodging
11/15 V = $1100
V = $1500