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.