Question

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 ?$64,640. How many tickets of each kind have been? sold?

$10 tickets sold?

$20 tickets sold?

$30 tickets sold?

Answer 1

Let suppose the number of tickets of $10, $20 and VIP be X Y and Z respectively

Hence.

X+Y+Z = 357 (as total tickets are 357) ....Equation 1

Now $20 tickets sold 157 more than $10 hence

Y = 157 + X ..equation 2

Total sales of tickets is $64,640 hence

10X + 20Y + 30Z = 64,640....Equation 3

Now lets put the value of X of Equation 2 in equation 1 and 3

X + Y + Z = 3,357 ..... X+X+157+Z = 3,357....Equation 4

10X + 20Y + 30Z = 64,640 ..... 10X+20 (X+157)+30Z= 64,640....Equation 5

Now we get the follwoing figures after solving the equation 4 and 5 (Please let me know if you need the working)

X=1150

Y=1307

Z=900

Thanks