Tickets cost $10.00, $20.00, and $30.00. 547 tickets were sold. 150 more $20.00 dollar tickets were sold than $ 10.00 tickets.The total sales were $9900.

Question

Tickets cost $10.00, $20.00, and $30.00. 547 tickets were sold. 150 more $20.00 dollar tickets were sold than $ 10.00 tickets.The total sales were $9900. how many tickets of each were sold?

Answer 1

 

 Let X be the number of $10 tickets (because X is the roman numeral for 10)

 Let J be the  number of $20 tickets (because J stands for Jackson and Andrew Jackson is on the $20 bill)

 Let T be the number of $30 tickets

 

X + J + T = 547 <--- 547 tickets were sold

 

J = X + 150 <-- there were 150 more twenty dollar tickets than $10 tickets

 

10X +20J +30T = 9900  <--- total sales were $9900

 

Substituting J=X+150 into

equations 1 and 3, the system becomes:

 

 X + X+150 + T = 547

 

10X + 20(X+150) + 30T = 9900

 

 

combining like terms and distributing:

 

2X + 150 + T = 547

 

10X + 20X + 3000 + 30T = 9900

 

Finally:

 

2X + T = 397

 

30X + 30T = 6900

 

 

Dividing the second equation by 30 and

solving the first equation for T:

 

T = 397 - 2x

 

X + T = 230

 

By substitution:

 

X + 397 - 2X = 230

 

0 = 230 - X - 397 + 2X

 

0 = X - 167

 

X = 167

 

T = 397 - 2X = 397 - 2(167) =  63

 

Finally using the original first equation

 

X + J + T = 547

 

167 + J  + 63 = 547

 

J = 547 - 167 - 63 = 317

 

167 x $10 + 317 x $20 + 63 x $30 = $9900

 

 

 

 

 

 

Answer 2

x = # $10 tickets

y = # $20 tickets

z = # $30 tickets

 

x+y+z = 547

y = x + 150

10x + 20y + 30z = 9900

 

Since we know y=x+150 we can substitute

that in the other 2 equations

 

x + x + 150 + z = 547

2x + z = 397

 

10x + 20(x+150) + 30z = 9900

30x + 3000 + 30z = 9900

30x + 30z = 6900

30(x+z) = 6900

x + z = 230

 

2x + z = 397

 x + z = 230   subtract from other equation

------------------

x = 167

 

x + z = 230

167 + z = 230

z = 63 

 

y = x + 150

y = 167 + 150

y = 317

 

167 tickets were $10

317 tickets were $20

63 tickets were $30