Question

at a museum, adult admission is $15.00 and children admission is $5.75. during one day, a total of 1800 adult and children admissions were collected, and $16,825 in admission fees was collected. how many adult admissions were collected? there were adult admissions.

Explanation:

Step1: Let variables

Let $x$ be the number of adult admissions and $y$ be the number of children admissions.
We have two - equations based on the given information:
Equation 1 (total number of admissions): $x + y=1800$, so $y = 1800 - x$.
Equation 2 (total admission fees): $15x+5.75y = 16825$.

Step2: Substitute $y$ into the second - equation

Substitute $y = 1800 - x$ into $15x + 5.75y=16825$:
$15x+5.75(1800 - x)=16825$.
Expand the equation: $15x+10350-5.75x = 16825$.

Step3: Combine like - terms

Combine the $x$ terms: $(15x-5.75x)+10350 = 16825$.
$9.25x+10350 = 16825$.

Step4: Solve for $x$

Subtract 10350 from both sides: $9.25x=16825 - 10350$.
$9.25x = 6475$.
Divide both sides by 9.25: $x=\frac{6475}{9.25}=700$.

Answer:

700