SOLUTION: Ann and Sean, paid $208 for concert tickets. They bought twice as many balcony tickets as floor tickets. Balcony tickets cost $15 each and floor cost $22 each. How many of each typ

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Ann and Sean, paid $208 for concert tickets. They bought twice as many balcony tickets as floor tickets. Balcony tickets cost $15 each and floor cost $22 each. How many of each typ      Log On


   

Question 437255: Ann and Sean, paid $208 for concert tickets. They bought twice as many balcony tickets as floor tickets. Balcony tickets cost $15 each and floor cost $22 each. How many of each type of ticket did they purchase ?
I have actually figured out the problem to be 8 balcony and 4 floor. The problem is that work has to be shown in algebraic form and I can't figure out how to set the problem up in algebraic form.
Found 2 solutions by ankor@dixie-net.com, nerdybill:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Ann and Sean, paid $208 for concert tickets.
They bought twice as many balcony tickets as floor tickets.
Balcony tickets cost $15 each and floor cost $22 each.
How many of each type of ticket did they purchase?
:
Let b = no. of balcony tickets
Let f = no. of floor tickets
:
Write an equation for each statement:
:
"Ann and Sean, paid $208 for concert tickets."
15b + 22f = 208
:
"They bought twice as many balcony tickets as floor tickets."
b = 2f
:
In the 1st equation, replace b with 2f
15(2f) + 22f = 208
30f + 22f = 208
52f = 208
f = 208%2F52
f = 4 floor tickets
Then
b = 2(4)
b = 8 balcony tickets


Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Ann and Sean, paid $208 for concert tickets. They bought twice as many balcony tickets as floor tickets. Balcony tickets cost $15 each and floor cost $22 each. How many of each type of ticket did they purchase ?
.
Let x = number of floor tickets
then from "They bought twice as many balcony tickets as floor tickets."
2x = number of balcony tickets
.
Our equation comes from:
"Balcony tickets cost $15 each and floor cost $22 each." and the fact that they paied $208:
15(2x) + 22x = 208
30x + 22x = 208
52x = 208
x = 4 (floor tickets)
.
balcony tickets:
2x = 2(4) = 8