SOLUTION: bill & jose's discount cinema sold adults' tickets for $4.10 each and children's tickets for $2.70 each. last tuesday, a total of $331.30 was collected from 89 movie watchers. how

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: bill & jose's discount cinema sold adults' tickets for $4.10 each and children's tickets for $2.70 each. last tuesday, a total of $331.30 was collected from 89 movie watchers. how       Log On


   

Question 248836: bill & jose's discount cinema sold adults' tickets for $4.10 each and children's tickets for $2.70 each. last tuesday, a total of $331.30 was collected from 89 movie watchers. how many of each type of ticket were sold? (let x represent the number of adults' tickets and y represent the number of children's tickets.)
4. solve by applying the quadratic formula. show your work. 3x2 - 2x + 3 = 0.
Found 2 solutions by josmiceli, tutorcecilia:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = number of adult tickets sold
Let y = number of children's tickets sold
given:
410x+%2B+270y+=+33130 (in cents)
(1) 41x+%2B+27y+=+3313
(2) x+%2B+y+=+89
Multiply both sides of (2) by 27
and subtract from (1)
(1) 41x+%2B+27y+=+3313
(2) -27x+-+27y+=+-2403
14x+=+910
x+=+65
and, since
x+%2B+y+=+89
65+%2B+y+=+89
y+=+89+-+65
y+=+24
65 adult tickets and 24 children's tickets were sold
check:
(1) 41x+%2B+27y+=+3313
41%2A65+%2B+27%2A24+=+3313
2665+%2B+648+=+3313
3313+=+3313
OK

Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
Use: x+y=total items
So, x+y=89
y=89-x
and
Use: ax+by=(total)(ratio)
So, 4.10x+2.70y=331.30
4.10x+2.70(89-x)=331.30[substitute y=89-x)
4.10x+240.30-2.70x=331.30
4.10x-2.70x=331.30-240.30
1.40x=91
x=91/1.40
x=65 adult tickes
65+y=89
so,
y=89-65=24 children tickets sold