Answer
In the amusement park, 1500 children and 700 adults were admitted that day.
Work Step by Step
Let's assume that $x$ number of children and $y$ number of adults were admitted. As $2200$ people entered the park that day, Therefore-
$x+y$ = $2200$ __eq.1
Now the fee for one child is $ 1.50$ Dollar and fee for one adult is $ 4.00$ Dollar, and total collection of the day was $5050$ Dollars. Therefore-
$1.5 \times x +4 \times y$ = $5050$
i.e. $1.5 x +4 y$ = $5050$ __eq.2
Substituting for $x$ in eq.2 from eq.1-
$1.5 (2200-y) +4 y$ = $5050$
i.e. $3300-1.5y + 4y$ = $5050$
i.e. $3300+ 2.5 y$ = $5050$
i.e. $2.5 y$ = $5050-3300$ = $1750$
i.e. $y$ = $\frac{1750}{2.5}$ = $700$
Substituting for $y$ in eq.1-
$x+700$ = $2200$
i.e. $x$ = $2200-700$ = $1500$
Thus in the amusement park, 1500 children and 700 adults were admitted that day.
