Question

Admission to the museum is $12 for children and $15 for adults. On a certain day 2450 people go the the museum and $33,456 is collected

How many adults and children went to museum

___children
___adults

Answer 1

`x-\ number\ of\ children\\y-\ number\ of\ adults\\\\ \left \{ {{x+y=2450} \atop {12x+15y=33456}} \right. \\\\ \left \{ {{x=2450-y} \atop {12x+15y=33456}} \right. \\\\ substitution\ method\\\\ 12(2450-y)+15y=33456\\\\29400-12y+15y=33456\\\\ 29400+3y=33456\ \ \ \ | subtract\ 29400\\\\ 3y=4056\ \ \ \ | divide\ by\ 3\\\\y=1352\\\\ x=2450-1352=1098\\\\ There\ were\ 1098\ children\ and\ 1352\ adults.`

Answer 2

c = children
a = adults

12c + 15a = 33456 (price)
c + a = 2450 (people)
c = 2450 - a (rewrite^)

12(2450 - a) + 15a = 33456 (substitute into the price equation)
29400 - 12a + 15a = 33456
3a = 4056
a = 1352

c = 2450 - (1352)
c = 1098

1098 children
1352 adults