Question

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 314 people entered the park, and the admission fees collected totaled 846.00 dollars. How many children and how many adults were admitted?

Answer 1

152 children and 162 adults were admitted

Explanation:

variables

• x = number of children
• y = number of adults

we know two equations just from the question

• x + y = 314 (number of children plus number of adults equals total number of people at the amusement park)
• 1.50x + 4y = 846 ((cost for children multiplied by number of children) plus (cost for adults multiplied by number of adults) equals total admission fees)

we first figure out the value for y from the first equation

• x + y = 302
• x - x + y = 302 - x
• y = 302 - x

now, we replace y in the second equation

• 1.50x + 4y = 828
• 1.50x + 4(302 - x) = 828
• 1.50x + 1208 - 4x = 828
• 1208 - 2.5x = 828
• 1208 - 828 = 2.5x
• 380 = 2.5x
• x = 152

we solved for the number of children, now we can just plug x to either equations and then solve for y which is the number of adults.

• x + y = 314
• 152 + y = 314
• y = 162

hope this helps!!