SOLUTION: a theather sold 478 tickets for a play . thickets cost $20 for adults and $13 for senior citizens.,if the total sreceips were $6970, how many senior citizen tickets were sold?

Question 174173: a theather sold 478 tickets for a play . thickets cost $20 for adults and $13 for senior citizens.,if the total sreceips were $6970, how many senior citizen tickets were sold?
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=# of adult tickets and y=# of senior tickets

"a theater sold 478 tickets for a play" translates to

and

"thickets cost $20 for adults and $13 for senior citizens.,if the total receipts were $6970" translates to

So we have the system of equations:

Let's solve the system by substitution

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

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

Since , we can now replace each in the second equation with to solve for

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Combine like terms on the left side

Subtract 6214 from both sides

Combine like terms on the right side

Divide both sides by 7 to isolate x

Divide

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and

So this means that 108 adult tickets and 370 senior tickets were sold.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
a theather sold 478 tickets for a play . thickets cost $20 for adults and $13 for senior citizens.,if the total receipts were $6970, how many senior citizen tickets were sold?
-------------------------
Quantity Equation: a + s = 478
Value Equation: 20a + 13s = 6970
-------------------------
20a + 20s = 9560
20a + 13s = 6970
------------------------
Subtract 2nd from 1st to get:
7s = 2590
370
s = 370 (# of senior tickets sold)
=====================================
Cheers,
Stan H.
RELATED QUESTIONS
I need help with these two word problems. I can not figure them out. 1. Adult tickets (answered by piyu)
University theater sold 515 tickets for a play. Tickets cost $20 per adult and $13 per... (answered by mananth,MatrixWoman)
university theater sold 444 tickets for a play. Tickets cost $20 per adult and $15 per... (answered by nyc_function)
University Theater sold 445 tickets for a play. Tickets cost $20 per adult and $12 per... (answered by stanbon,Alan3354)
Tickets for an event cost $5 for children, $10 for adults, and $8 for senior citizens.... (answered by ankor@dixie-net.com)
Tickets for an event cost $4 for children, $12 for adults, and $7 for senior citizens.... (answered by stanbon)
Tickets for an event cost $4 for children, $12 for adults, and $7 for senior citizens.... (answered by ankor@dixie-net.com)
Tickets for an event cost $4 for children, $12 for adults, and $7 for senior citizens.... (answered by ankor@dixie-net.com)
Tickets for an event cost $5 for children, $11 for adults, and $6 for senior citizens.... (answered by ptaylor)