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Question 286385: What information is needed to solve the following problem?
For the senior play, twice as many adult tickets as student tickets were sold. If $4.20 was collected, how many student tickets were sold?
A. cost only of adult tickets
B. all needed information is given
C. cost of each type of ticket
D. the title of the play
Found 2 solutions by Theo, richwmiller:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Your answer is selection D.
You need the cost of each type of ticket.
You are given:
$4.20 was collected.
Number of Adult Tickets sold is 2 * the number of Student Tickets sold.
Let a = number of adult tickets sold.
Let s = number of student tickets sold.
Your first equation is a = 2*s
Your second equation is:
a*x + s*y = $4.20 where x = cost of each adult ticket and y = cost of each student ticket.
Since you know that a = 2*s, you can substitute 2*s for a in the equation to get:
2*s*x + s*y = $4.20 which becomes s*(2*x + y) = $4.20.
Divide both sides of this equation by s to get:
2*x + y = $4.20/s
If you know the value of x and y, then you can solve for s.
Once you can solve for s, then you can solve for a.
Example:
let x = .09 and y = .02
This means that each adult ticket cost 9 cents and each student ticket cost 2 cents.
Equation becomes:
2*.09 + .02 = 4.20/s
This becomes:
.2 = 4.20/s
Solve for s to get:
s = 4.2/.2 = 21
a = 2*s means a = 42.
42 adult and 21 student tickets were sold, given that each adult ticket was .09 and each student ticket was .02.
(42 * $.09) + (21 * .02) = $3.78 + $.42 = $4.20
You couldn't solve this unless you knew the cost of each adult ticket and the cost of each student ticket.
Now, if you know the cost of each adult ticket and the number of student tickets sold, then you could have also solved this problem, but that was not one of the selections you were given.
Example
Same equation of:
2*x + y = $4.20/s except this time you are given:
Cost of an adult ticket = $.09
Number of student tickets sold = 21.
You would substitute in the equation to get:
2*.09 + y = $4.20/21 which would become:
$.18 + y = $.20
Subtract .18 from both sides of this equation to get:
y = $.20 - $1.8 = $.02
From there the problem is solved.
x = $.18
y = $.02
s = 21
a = 2*s = 42.
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! a=2s
a*C+s*c=4.20
if we knew the cost of each ticket we could solve.
We have two equations and 4 unknowns
We need an equation for each unknown
so we need two more knowns to have two equations in two unknowns
Answer C. cost of each type of ticket.
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