SOLUTION: A basketball team sells tickets that cost​ $10, $20,​ or, for VIP​ seats,​ $30. The team has sold 3357 tickets overall. It has sold 157 more​ $20 tick

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Question 1119157: A basketball team sells tickets that cost​ $10, $20,​ or, for VIP​ seats,​ $30. The team has sold 3357 tickets overall. It has sold 157 more​ $20 tickets than​ $10 tickets. The total sales are ​$64 comma 64,640. How many tickets of each kind have been​ sold?
# $10 tickets sold
# $20 tickets sold
# $30 tickets sold
Found 3 solutions by ankor@dixie-net.com, ikleyn, josgarithmetic:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
let a = no. of $10 ticket
let b = no. of $20 tickets
let c = no. $30 tickets
:
Write an equation for each statement
:
A basketball team sells tickets that cost​ $10, $20,​ or, for VIP​ seats,​ $30.
The total sales are 64,640.
10a + 20b + 30c = 64640
simplify divide by 10
a + 2b + 3c = 6464
:
The team has sold 3357 tickets overall.
a + b + c = 3357
:
It has sold 157 more​ $20 tickets than​ $10 tickets.
b = a + 157
-a + b = 157
:
How many tickets of each kind have been​ sold?
:
We solve this as a matrix using that feature on a ti83 or similar
a + 2b + 3c = 6464
a + b + c = 3357
-a + b + 0 = 157
enter
1, 2, 3, 6464
1, 1, 1, 3357
-1,1 0 = 157
Resulting in
a = 1150
b = 1307
c = 900
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
This problem is for ONE unknown. 

Let x = #of $10 tickets.

Then the number of $20 tickets is (x+157).

Then the number of $30 tickets is the rest  3357 - x - (x+57) = 3300-2x.


The money equation is

10x + 20*(x+57) + 30*(3300-2x) = 64640.


Simplify and solve for x.


The lesson to learn from this solution: 

    This problem is for ONE unknown - not for three.


        This problem is for ONE unknown - not for three.


            This problem is for ONE unknown - not for three.

----------------
To see many other similar solved problems, look into the lesson
    - Advanced word problems to solve using a single linear equation
in this site.


Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
x, number of $10 tickets
y, number of $20 tickets
z, number of $30 tickets

Exact translation of the description:


Simplifying the system:


Eliminating x is easily done:




Subtract to eliminate z:


Find x:







Finish for z:





checking the revenue:



SOLUTION:
1150 of the $10 tickets
1307 of the $20 tickets
900 of the $30 tickets
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