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?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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?      Log On


   

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) About Me  (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 x%2By=478

and


"thickets cost $20 for adults and $13 for senior citizens.,if the total receipts were $6970" translates to 20x%2B13y=6970






So we have the system of equations:


system%28x%2By=478%2C20x%2B13y=6970%29


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

x%2By=478 Start with the first equation


y=478-x Subtract x from both sides


y=-x%2B478 Rearrange the equation


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

Since y=-x%2B478, we can now replace each y in the second equation with -x%2B478 to solve for x



20x%2B13highlight%28%28-x%2B478%29%29=6970 Plug in y=-x%2B478 into the second equation. In other words, replace each y with -x%2B478. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



20x%2B%2813%29%28-1%29x%2B%2813%29%28478%29=6970 Distribute 13 to -x%2B478


20x-13x%2B6214=6970 Multiply


7x%2B6214=6970 Combine like terms on the left side


7x=6970-6214Subtract 6214 from both sides


7x=756 Combine like terms on the right side


x=%28756%29%2F%287%29 Divide both sides by 7 to isolate x



x=108 Divide





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


So the first part of our answer is: x=108









Since we know that x=108 we can plug it into the equation y=-x%2B478 (remember we previously solved for y in the first equation).



y=-x%2B478 Start with the equation where y was previously isolated.


y=-%28108%29%2B478 Plug in x=108


y=-108%2B478 Multiply


y=370 Combine like terms



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


So the second part of our answer is: y=370









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

So our answers are:

x=108 and y=370


So this means that 108 adult tickets and 370 senior tickets were sold.

Answer by stanbon(75887) About Me  (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.