|
Question 1003069: A movie theater charges $9.50 for an adult and $7.75 for a child to see a movie. If 92 people were at the 9:20 pm show and the total admission paid was $837.25, how many adult tickets were at the movies?
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website!
x= number of adults
y= number of children
Total comercials
1.00 x + 1.00 y = 92.00 .............1
Total value
9.50 x + 7.75 y = 837.25 .............2
Eliminate y
multiply (1)by -7.75
Multiply (2) by 1.00
-7.75 x -7.75 y = -713.00
9.50 x + 7.75 y = 837.25
Add the two equations
1.75 x = 124.25
/ 1.75
x = 71.00
plug value of x in (1)
1.00 x + 1.00 y = 92.00
71.00 + y = 92.00
y = 92.00 -71.00
y = 21.00
y = 21.00
x= 71 number of adults
y= 21 number of children
m.ananth@hotmail.ca
Answer by ikleyn(53646)  (Show Source):
You can put this solution on YOUR website! .
A movie theater charges $9.50 for an adult and $7.75 for a child to see a movie.
If 92 people were at the 9:20 pm show and the total admission paid was $837.25,
how many adult tickets were at the movies?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In this problem, they ask about the number of adult tickets, only.
So, there is no need to work with two unknowns and solve a system of two equations.
One unknown and one equation is enough, as I will show below in my solution.
It simplifies the methodology and make calculations/solution/writing shorter.
Let x be the number of adult tickets.
Then the number of child tickets was (92-x).
Write an equation for the total revenue
7.75x + 9.50(92-x) = 837.25.
Simplify and find x
7.75x + 9.50*92 - 9.50x = 837.25,
7.75x - 9.50x = 837.25 - 9.50*92,
-1.75x = -36.75,
x =  = 21.
ANSWER. The number of the child tickets is 21.
CHECK. Let's check the total revenue: 7.75*21 + 9.50*(92-21) = 837.25. ! Precisely correct !
Solved, using only one unknown and one equation.
Less calculations and shorter writing.
|
|
|
| |
