SOLUTION: The admission fee for Knoebels amusement park is $5 for children and $9 for adults. On a certain day, 450 people enter the park and the admission fees collected totaled $3,050. How

Question 270719: The admission fee for Knoebels amusement park is $5 for children and $9 for adults. On a certain day, 450 people enter the park and the admission fees collected totaled $3,050. How many children and how many adults were admitted?
(Here's what I tried):
Variables:
c= Child admission
a= Adult admission
c+a=450
$5c+$9a=$3,050
changed c+a=450 to c=450-a
substitution:
$5(450-a)+$9a=$3,050
Not sure if my equations are right. Based off of how I solved a similiar problem. And I don't know how to simplify from there.
Could you please tell me if I'm on the right track and if so, how to solve from where I stopped?
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
Great progress so far:
c= Child admission
a= Adult admission
c+a=450
$5c+$9a=$3,050
changed c+a=450 to c=450-a
substitution:
$5(450-a)+$9a=$3,050
Not sure if my equations are right. Based off of how I solved a similiar problem. And I don't know how to simplify from there.
Could you please tell me if I'm on the right track and if so, how to solve from where I stopped?
So starting from where you left off:
5(450-a) + 9a = 3050
2250 - 5a + 9a = 3050
9a - 5a = 3050 - 2250
4a = 800
a = 200
c = 450 - a
c = 450 - 200
c = 250

RELATED QUESTIONS
The admission fee at an amusement park is $ 1.50 for children and $ 4.00 for adults. On a (answered by ewatrrr)

The admission fee at an amusement park is $20 for children and $35 for adults. On a... (answered by josgarithmetic,ikleyn)

The admission fee at an amusement park is $4.00 for children and $7.20 for adults. On a... (answered by josgarithmetic)

The admission fee at an amusement park is $2.00 for children and $5.20 for adults. On a... (answered by josgarithmetic,ikleyn)

The admission fee at an amusement park is $3.50 for children and $5.60 for adults. On a... (answered by josgarithmetic)

The admission fees at an amusement park are $2.50 for children and $5.20 for adults. On a (answered by Edwin McCravy)

The admission fees at an amusement park are $2.50 for children and $5.20 for adults. On a (answered by ikleyn)

The admission fee at an amusement park is $3.50 for children and $5.80 for adults. On a... (answered by CubeyThePenguin)

The admission fee at an amusement park is $3.75 for children and $5.00 for adults. On a... (answered by CubeyThePenguin)