Answer:
176 children and 105 adults.
Step-by-step explanation:
Let's call x the number of children and y the number of adults.
If 281 people entered the park, we can write the following equation
x + y = 281
If they collected 684 dollars, we can write the following equation
1.5x + 4y = 684
because it cost $1.5 for children and $4 for adults.
Now, we have the following system of equations
x + y = 281
1.5x + 4y = 684
First, we need to solve the first equation for y, so
x + y = 281
x + y - x = 281 - x
y = 281 - x
Then, replace this expression on the second equation
1.5x + 4y = 684
1.5x + 4(281 - x) = 684
1.5x + 4(281) - 4(x) = 684
1.5x + 1124 - 4x = 684
-2.5x + 1124 = 684
Finally, we can solve the equation for x
-2.5x + 1124 - 1124 = 684 - 1124
-2.5x = -440
-2.5x/(-2.5) = -440/(-2.5)
x = 176
So, the value of y is equal to
y = 281 - x
y = 281 - 176
y = 105
Therefore, they admitted 176 children and 105 adults.