Question 1204593: Isabella is buying tickets to a concert. Adult tickets (x) cost $45 each and children tickets (y) cost $37 each. Isabella spent a total of $521 and purchased 3 more children tickets than adult tickets. Which is a viable solution for the system of equations?
Found 4 solutions by josgarithmetic, ikleyn, mananth, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!
PRICE HOW MANY COST
ADULT TICKETS 45 x 45x
CHILD TICKETS 37 x+3 37(x+3)
Totals 521
You will most likely understand that, and know what to do.
You wanted a SYSTEM of equations?
PRICE HOW MANY COST
ADULT TICKETS 45 x 45x
CHILD TICKETS 37 y 37y
Totals 521
AND y-x=3
This way you would have  .
Answer by ikleyn(52785)  (Show Source):
You can put this solution on YOUR website! .
Isabella is buying tickets to a concert. Adult tickets (x) cost $45 each
and children tickets (y) cost $37 each. Isabella spent a total of $521
and purchased 3 more children tickets than adult tickets.
 What is a  solution for the system of equations?
~~~~~~~~~~~~~~~~~~~~~~~~~~
The system of equation is
y - x = 3 tickets (1)
45x + 37y = 521 dollars (2)
To solve it, from equation (1) express y = 3+x and substitute it into equation (2).
You will get then
45x + 37(3+x) = 521.
Simplify and find x
45x + 111 + 37x = 521
45x + 37x = 521 - 111
82x = 410
x = 410/82 = 5 (number of adult tickets)
Then y = 3+x = 3+5 = 8 (number of children tickets)
ANSWER. 5 adult tickets and 8 children tickets.
CHECK. 5*45 + 8*37 = 521 dollars, total money spent for tickets. ! correct !
Solved.
Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website! Isabella is buying tickets to a concert. Adult tickets (x) cost $45 each and children tickets (y) cost $37 each. Isabella spent a total of $521 and purchased 3 more children tickets than adult tickets. Which is a viable solution for the system of equations?
Adult tickets (x) cost $45 each and children tickets (y) cost $37 each.
3 more children tickets than adult tickets.
y=x+3
Isabella spent a total of $521
45x +37y= 521
y=x+3
y-x=3 ( multiply by 45)
45y-45x= 135
45x +37y= 521
Add the two equataions
we get 82y = 656
y=8
So x=5
x=5 (number of adult tickets) and
y=8 (number of children tickets).
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Your question "Which is a viable solution for the system of equations" is very strange....
The "viable solution" to a system of equations is THE solution to that system of equations.
Presumably you were given some examples of systems of equations that might BE USED TO SOLVE the problem, and you were supposed to choose the one which was a valid setup. But in that case, for us to answer your question, you would have to show us those examples.
Without seeing those examples, the simplest set of equations is
(1) 45x+37y=521 (total cost of x tickets at $45 each and y tickets at $37 each is $521)
(2) y=x+3 (the number of children tickets is 3 more than the number of adult tickets)
As for the solution for the numbers of adult and children tickets, with the two equations in that form it seems substitution would be the most straightforward solution method:
45x+37(x+3)=521
and go from there.
For a quick informal solution (which is good mental exercise), you can do this:
The "extra" 3 children tickets cost 3($37) = $111, so the remaining tickets (equal numbers of adult and children tickets) cost $521-$111=$410. Since one adult ticket and one children ticket cost $45+$37 = $82, the number of each kind of ticket is $410/$82 = 5.
So she bought 5 adult tickets and 5+3 = 8 children tickets.
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