Question 698970: mr.santos treated his students to a movie for winning the state contest. this also required taking some of the students parents as chaperones. the movie theater charges 4 dollars for each student and 6 dollars for each adult. if mr.santos spent 180 dollars on movie tickets and took 40 people( including himself ), how many students and how many adults went to see the movie?
Need to write s system of equations for the word problem above and then solve three ways (graphing AND substitution AND elimination).
Found 2 solutions by mananth, stanbon:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! x= number of student tickets
y= number of adult tickets
Total sold
4 x + 6 y = 180 .............1
1 x + 1 y = 40 .............2
Eliminate y
multiply (1)by 1
Multiply (2) by -6
4 x 6 y = 180
-6 x -6 y = -240
Add the two equations
-2 x = -60
/ -2
x = 30
plug value of x in (1)
4 x + 6 y = 180
120 + 6 y = 180
6 y = 180 -120
6 y = 60
y = 10
x= 30 number of student tickets
y= 10 number of adult tickets
Substitution
1 x + 1 y = 40 .............1
1 y = 40 + -1 x
/ 1 =
y = 40 + -1 x
4 x + 6 y = 180 .....................2
Substitute y in (2)
4 x + 6 ( 40 + -1 x ) = 180
4 x + 240 + -6 x = 180
4 x -6 x = -60
-2 x = -60
/ -2
x= 30
Plug the value of x in (1)
1 x + 1 y = 40
1 * 30 + 1 y = 40
30 + 1 y = 40
1 y = 10
/ 1
y= 10
x= 30 number of student tickets
y= 10 number of adult tickets
Graph
1 x + 1 y = 40 .............1
4 x 6 y = 180 .............2
Find the x & y intercept points by plugging x=0,y=0 in both equations.
equation I
when x= 0 y= 40 ,( 0 , 40 )
when y = 0 x= 40 ,( 40 , 0 )
Equation 2
when x= 0 y= 30 ( 0 , 30 )
when y = 0 x= 45 ( 45 , 0 )
You will observe that the point of intersection is 30,10
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! mr.santos treated his students to a movie for winning the state contest. this also required taking some of the students parents as chaperones. the movie theater charges 4 dollars for each student and 6 dollars for each adult. if mr.santos spent 180 dollars on movie tickets and took 40 people( including himself ), how many students and how many adults went to see the movie?
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People equation: a + s = 40
Value equation::6a +4s = 180
------------------------------
Simplify:
a = -s+40
a = (-2/3)s + 30
--------
Substitute:
-s+40 = (-2/3)s+30
(1/3)s = 10
s = 30
---
a = -s+40 = 10
-------------------------
Elimination:
3a + 3s = 3*40
3a + 2s = 90
----
Subtract and solve for "s":
s = 120-90 = 30
---
3a + 2s = 90
3a + 60 = 90
3a = 30
a = 10
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Cheers,
Stan H.
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