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. The following system of equations models this scenario: x + y = 224 12x + 8y = 2,520 How many visitors were 18 or younger? 42 56 182 194

Answer 1

let x be the number of visitors younger than 18 yrs

let y be the number of visitors older than 18 yrs

according to first condition

8x+12y=2520.....(1)

according to second condition

x+y=224..... (2)

multiplying equation 2 by 8

8x+8y=1792....(3)

subtracting equation 3 from 2

8x+12y=2520....(2)

-8x-8y=-1792.... (3)

__________

4y =728

y=182

putting y=182 in equation 2

8x+12y=2520

8x+12×182=2520

8x+2184=2520

8x=2520-2184

8x=336

x=42

Therefore 42 visitors are 18 yrs or younger