at a benefit concert, 600 tickets were sold and $1500 was raised. if there were $2 and $5 tickets, how many each where sold

Question

at a benefit concert, 600 tickets were sold and $1500 was raised. if there were $2 and $5 tickets, how many each where sold

Answer 1

Let X = number of $2 tickets sold

Let Y = number of $5 tickets sold

 

600 tickets were sold  ==>  X + Y = 600  ==>  X = 600 - Y

 

$1500 was raised  ==>  2X + 5Y = 1500

 

Plug the expression for X from the 1st equation in to the 2nd equation and solve 

 

2(600 - Y) + 5Y = 1500

1200 - 2Y + 5Y = 1500

3Y = 300

Y = 100

 

So X = 600 - Y = 600 - 100 = 500

 

There were 500 tickets sold for $2 each and 100 tickets sold for $5 each 

 

Check:  500 + 100 = 600 tickets total

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