For clarification, I am going to assume the "you guys are behind 30,000 bucks" statement means that the five people each have a budget of $30,000, just so that the problem can seem to make sense. (If we were to assume the total budget for the five people was just $30,000, there would be too little money to even send all 5 to Starbucks.) If this assumption is not true, please correct me and I will try to redo it.
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For a word problem, we need to first understand what it contains and wants from us. The problem tells us that we need to split five people into going to Starbucks or to a baseball game. Let's show the number of people going to either Starbucks or baseball as two variables — s for people going to Starbucks and b for going to baseball. The problem also tells us that we have $30,000 per person for our budget, so we can multiply this number by 5 to get our combined budget of $150,000.
Now let's deal with the traveling costs. The problem tells us that it takes 15 miles per person to go from home to Starbucks, and 60 miles per person from home to the baseball game. We are also told that for each person it costs $6000 to travel per day, and for each day they travel 10 miles. We need to convert the miles to money in cost so that we can determine how we distribute the people with our budget, se we need to use the conversions they give us:
($6000 / day) • (1 day / 10 miles) = $6000 / 10 miles = $600 / mile
Note how the day variable gets canceled out.
Now that we have this ratio we can convert the travel costs from miles to money.
Starbucks: (15 miles / person) • ($600 / mile) = $9,000 / person
Baseball: (60 miles / person) • ($600 / mile) = $36,000 / person
So for each person, it costs a certain amount to travel to a location. Since we need to stay within the budget, we need to express this as an inequality:
9,000s + 36,000b ≤ 150,000
We also know we only have 5 people to distribute. Let's show this as a second equation:
s + b = 5
Now we just need to substitute and solve.
s = 5 − b
9,000(5 − b) + 36,000b ≤ 150,000
45,000 − 9,000b + 36,000b ≤ 150,000
45,000 + 27,000b ≤ 150,000
27,000b ≤ 105,000
b ≤ 3.88888...
s + (3.88888...) = 5
s ≈ 1.11111...
Unfortunately we can't split apart one person into 0.888888th of a person to use all of our budget, so we'll have to stick with whole numbers. We can round down b to 3 and s up to 2.
Remember that our inequality states that b can't be more than 3.88888... so rounding up to 4 isn't possible.
Checking out work:
9,000(2) + 36,000(3) ≤ 150,000
126,000 ≤ 150,000
Hope this helps!
