Let the cost of admission for an adult be A, and the cost of admission for a child be C.
Then let us translate the story from English to Algebra.
4A + 3C = 403 (the cost of admission to a theme park was $403 for 4 adults and 3 children)
8A + 2C = 690 (the admission was $690 for 8 adults and 2 children)
Now we can solve the system of equations for example as follows
4A + 3C = 403 (we left the first equation as is)
4A + C = 345 (we divided both sides of the second equation by 2, i. e. half of the second party decided that the theme park was too expensive and went hiking instead)
2C = 58 (we subtracted the new second equation from the first, i.e. the two extra children in the first party resulted in extra $58 in admission costs)
4A + C = 345 (we left the second equation as is)
C = 29 (we divided both sides of the first equation by 2, i. e. if the admission for two children is $58, then admission for one child is $58/2 = $29)
4A + C = 345 (we left the second equation as is)
C = 29 (we left the first equation as is)
4A = 316 (we subtracted the first equation from the second)
Finally
C = 29 (we left the first equation as is)
A = 79 (we divided both sides of the second equation by 4)
and translating the results back to English
Cost of admission for an adult is $79 and for a child is $29
