Answer:
3 adult tickets, 2 senior tickets, and 6 children's tickets
Step-by-step explanation:
Start by writing down the information they give you: they purchased 3 more children's tickets than adult tickets, 1 less senior ticket than adult tickets, total cost of $131. Now take all of that, and translate it into math terms.
3 more children's tickets than adult tickets can be represented by an expression like 3 + a, where a = adult tickets. 3 + a will give you the number of children tickets purchased.
1 less senior ticket than adult tickets can be written like a - 1, the number of adult tickets minus 1 because 1 less senior ticket was purchased.
Now, adult tickets cost $15, senior tickets cost $13, and children cost $10.
So now we can put together an equation like this:
10(3 + a) + 15(a) + 13(a - 1) = 131 ... that is, the number of children's tickets, 3 + a, times the cost of those tickets, 10, plus the number of adult tickets, a, times the cost of those tickets, 15, plus the number of senior tickets, a - 1, plus the cost of senior tickets, 13. From here, you just want to simplify.
30 + 10a + 15a + 13a - 13 = 131 ... multiply and distribute
38a + 17 = 131
38a = 114
a = 3
So they purchased 3 adult tickets.
Now that you know how many adult tickets you bought, you know that the number of senior tickets is the adults minus 1. So there were 2 senior tickets purchased. And since you know the number of adults tickets is 3, and that the number of children's tickets was three times the amount of adult tickets, then you know they bought tickets for 9 children because 3 + a = 3 + 3 = 6.
