Tickets cost $8.00 each for adults and $2.50 each for kids, and the group paid $46.50 in total. There were 6 fewer adults than kids in the group. Find the number of adults and kids on the trip.
# of adults =
# of kids =
5
2
Let's assume the number of kids in the group is "x".
Since there were 6 fewer adults than kids, the number of adults would be "x - 6".
We know that each adult ticket costs $8.00 and each kid ticket costs $2.50.
Therefore, the total cost of adult tickets is (x - 6) * $8.00, and the total cost of kid tickets is x * $2.50.
The total cost of all tickets is given as $46.50. So, we can set up the following equation:
(x - 6) * $8.00 + x * $2.50 = $46.50
Now we can solve this equation to find the value of x, which represents the number of kids in the group.
8(x - 6) + 2.5x = 46.5
Distribute the multiplication:
8x - 48 + 2.5x = 46.5
Combine like terms:
10.5x - 48 = 46.5
Add 48 to both sides:
10.5x = 94.5
Divide both sides by 10.5 to solve for x:
x = 9
Therefore, there are 9 kids in the group.
To find the number of adults, we substitute the value of x back into our initial assumption:
Number of adults = x - 6 = 9 - 6 = 3
Therefore, there are 3 adults and 9 kids in the group.