Question

the admission fee at an amusement park is $2.00 for children and $7.00 for adults. on a certain day, 299 people entered the park, and the admission fees collected totaled $1573. how many children and how many adults were admitted?

Answer 1

104 children and 195 adults

Explanation:

let a represent number of adults and c represent number of children , then

a + c = 299 → (1)

7a + 2c = 1573 → (2)

multiplying (1) by - 2 and adding to (2) will eliminate c

- 2a - 2c = - 598 → (3)

add (2) and (3) term by term to eliminate c

5a + 0 = 975

5a = 975 ( divide both sides by 5 )

a = 195

substitute a = 195 into (1) and solve for c

195 + c = 299 ( subtract 195 from both sides )

c = 104

104 children and 195 adults were admitted