A movie theater charges $ 8 for adults and $ 6 for seniors. On a particular day when 336 people paid an admission, the total receipts were $ 2598.
How many who paid were adults?
How many who paid were seniors?
I got this two equation (8x+6y=2598 and second equation is X+y=336) but I been trying to solve them and I can't I thing they might be written wrong.
Can some one please help me.
Your equations are correct.
To solve (By subtraction):
8x + 6y = 2598
-(x + y) * 6 = (336) * 6
________________________
2x + 0y = 582
Solve for x
(2x)/2 = (582)/2
x = 291
Solve for y:
x + y = 336
(291) + y = 336
(291) + y - (291) = 336 - (291)
y = 45
Solution (291,60)
Check Work:
8*(291) + 6*(45) = 2598
(291) + (45) = 336
To solve the system of equations:
Let x be the number of adults, and y be the number of seniors.
From the given information, we have the equations:
Equation 1: 8x + 6y = 2598
Equation 2: x + y = 336
To solve the equations, we can use either substitution or elimination method. Let's use the elimination method:
Multiply Equation 2 by 6 to make the coefficients of y in both equations the same:
6(x + y) = 6(336)
6x + 6y = 2016
Now, we have the following system of equations:
Equation 3: 8x + 6y = 2598
Equation 4: 6x + 6y = 2016
Subtract Equation 4 from Equation 3 to eliminate y:
(8x + 6y) - (6x + 6y) = 2598 - 2016
8x - 6x + 6y - 6y = 582
2x = 582
x = 291
Now, substitute the value of x into Equation 2 to find y:
291 + y = 336
y = 336 - 291
y = 45
Therefore, there were 291 adults who paid and 45 seniors who paid.
To solve this problem, you have correctly set up the two equations:
1) 8x + 6y = 2598 (equation for the total receipts)
2) x + y = 336 (equation for the total number of people)
To solve these equations, you can use a method called substitution or elimination. Let's use substitution in this case.
First, solve one equation for one variable in terms of the other variable. From equation 2, isolate x:
x = 336 - y (equation 3)
Now substitute this expression for x into equation 1:
8(336 - y) + 6y = 2598
Expanding the equation, you get:
2688 - 8y + 6y = 2598
Combine the like terms:
-2y = 2598 - 2688
-2y = -90
Divide by -2:
y = -90 / -2
y = 45
Now substitute the value of y = 45 back into equation 3 to find x:
x = 336 - 45
x = 291
Therefore, there were 291 adults (x) and 45 seniors (y) who paid for admission.