Question

The art museum had a total of 224 visitors on Tuesday. Visitors older than 18 paid $12 for admission. Visitors 18 years or younger paid $8 for admission. The museum collected a total of $2,520. How many visitors were 18 or younger? (2 points)

42
56
182
194

Answer 1

@AlexandervonHumboldt2

Answer 2

Let's say \(x\) is number of adult visitors (18 and older) and \(y\) of young visitors (18 or younger).
We know that in total they make 224. so we say:
$$
x + y = 224 \implies x = 224 - y
$$We also know that every adult visitor paid $12 and every young visitor paid $8. In total they all paid $2,520. So we say:
$$
12x + 8y = 2520
$$But as shown above, we can describe 'x' as (total_visitors - young_visitors). So:
$$
12(224-y) + 8y = 2520 \\
2688 - 12y + 8y = 2520 \\
-4y = 2520 - 2688 \\
-4y = -168 \\
y = \frac{168}{4} = 42
$$And we found \(y\), which is the number of the young visitors.
Hope it's clear.