Tickets to a show cost $10 in advance and $15 at the door. If 120 tickets are sold for a total of $1390, how many tickets were bought in advance?

Guest Apr 5, 2020

#1**+2 **

Here is how I solve it:

Say all the tix were bought in advance: that would mean 1200 dollars were sold. For each ticket we turn into bought at the door, we gain 5 dollars. The difference of 1390 and 1200 is 190. So 190/5 38 were bought at the door.* So 82 were bought in advance.*

Check

38*15=570

82*10=820

820+570=1390

MooMooooMooM Apr 5, 2020

#3**+2 **

We can solve this using a system of equations.

Let \(x=\)tickets bought at the door

Let \(y=\)tickets bought in advance

Our equations are

\(10y+15x=1390\)

\(y+x=120\)

We can solve elimination (Feel free to use a different strategy):

Multiply the bottom equation by \(10\)

\(10y+10x=1200\)

Subtract the bottom equation

\(5x=190\)

Divide both sides by \(5\)

\(x=38\)

Plug that value into the bottom equation (or the top if you want)

\(y+38=120\)

Subtract \(38\) from both sides

\(y=82\)

\(82\) tickets were bought at the door.

Hope this helped!!!

-Ako

Ako180 Apr 5, 2020