Question

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day,

336 people entered the park, and the admission fees collected totaled 854.00 dollars. How many
children and how many adults were admitted?

Answer 1

There were 108 children and 175 adults.


System of equations:

1.5x + 4y = 862
x + y = 283

Let's use substitution of the x variable to solve the system.

x + y = 283 <--- subtract x from both sides

y = 283 - x

Substitute y = 283 - x into the first equation.

1.5x + 4 (283 - x) = 862 <--- distribute 4 to 283 and -x

1.5x + 1132 - 4x = 862 <--- combine 1.5x and -4x

1132 - 2.5x = 862 <--- subtract 1132 from both sides

-2.5x = -270 <--- divide both sides by -2.5

x = 108

Substitute x =108 back into y = 283 - x

y = 283 - 108 = 175

There were 108 children and 175 adults.