SOLUTION: at a benefit concet, 600 tickets were sold and $1500 was raised. if there were $2 and $5 tickets, how many of each were sold?

Question 154505: at a benefit concet, 600 tickets were sold and $1500 was raised. if there were $2 and $5 tickets, how many of each were sold?
Found 2 solutions by BrittanyM, jojo14344:
Answer by BrittanyM(80) (Show Source): You can put this solution on YOUR website!
We can use the given information to set up a system of equations and find each of the variables.

We were told that there were a total of 600 tickets sold:

x + y = 600

And that one type of ticket was sold for two dollars while the other type was sold for five dollars. The total in sales was $1500.

2x + 5y = 1500

Now, we can manipulate the first equation to find x in terms of y.

x = 600 - y

And plug this into the second equation in order to solve for y.

2( 600 - y ) + 5y = 1500
1200 - 2y + 5y = 1500
3y = 300
y = 100

We can plug this value into either of the two equations to find the value for x.

x + 100 = 600
x = 500

So there were 100 five dollar tickets sold and 500 two dollar tickets sold, but just to be certain, we can plug these values back into either equation to check our answer.

2( 500 ) + 5( 100 ) = 1500
1000 + 500 = 1500

Since this is true, we know that our answers are correct.
Answer by jojo14344(1513) (Show Source): You can put this solution on YOUR website!
Let:
=no.of $2.00
=no.of $5.00
So, ---------------------------------> eqn 1
In eqn 1 we get, ---------------------------> eqn 2
Also, no.of tickets of $2.00 + no.of tickets of $5.00=$1500. To show in eqn,
--------------------------------> eqn 3
Substitute eqn 2 in eqn 3:

----->

---------------------------> total of $5.00 tickets
For $2.00 tickets, go back eqn 2:
-------------------> total of $2.00 tickets
In doubt? Go back eqn 3:

Thank you,
Jojo

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