can somebody solve this eq'n??

Question

a certain auditorium has a seating capacity of 1200. If drama group charges of $ 60.00 for adults and $ 40.00 for children, find the minimum number of adult tickets they should sell to cover their produtcion costs of $ 67,000.00 Solve using split point method.
pls.. i really need this for our assignment...

Answer 1

Let A = Adults
C = Children

A + C = 1200 ( seating capacity) -- 1
60A + 40C = 67000 -- 2

simplify eq 2 we get

3A + 2C = 3350 -- eq 3
A + C = 1200 -- eq 4

multiply eq 4 by -2
we get

3A + 2C = 3350
-2A -2C = -2400
--------------------- (adding both)
A = 950
C = 1200 - 950
= 250

Answer 2

Let

a = the amount of adults

c = the amount of children

1200 the seating capacity

60a The charges of the adult

40c The charges for the children

67000 The production cost

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a + c = 1200 - - - - - - - -Equation 1

60a + 40c = 67000 - - - -Equation 2

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The substitution Method equation 1

a + c = 1200

a + c - a = 1200 - a

c = 1200 - c

insert the c value into equation 2

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60a + 40c = 67000

60a + 40(1200 - a) = 67000

60a + 48000 - 40a = 67000

20a + 48000 - 48000 = 67000 - 48000

20a = 19000

20a/20 = 19000/20

a = 950 adutts

The answer is a = 950

Insert the a value into equation 1

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a + c = 1200

950 + c = 1200

559 + c = 1200 - 950

c = 250 Children

The answer is c = 250

Insert the c value into equation 1

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Check for equation 1

a + c = 1200

950 + 250 = 1200

1200 = 1200

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Check for equation 2

60a + 40c = 67000

60(950) + 40(250) = 67000

57000 + 10000 = 67000

67000 = 67000

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The total cost for the adults is $ 57000

The total cost for the children $ 10000

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The number of adults is 950

The number of children is 250

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Answer 3

First, set up the equations you need to use. You can write two algebraic equations from the information given. Let's denote adult tickets as 'A' and child tickets as 'C'. Thus, you can derive that:

(1) A+C=1200
(2) 60A+40C>=67,000

Two equations and two uknowns, now we can solve for minimum number of A

Solving for C in (1), you get C = 1200-A

Substitute this in (2), you get:
60A+40(1200-A)>=67000 -------> 60A+48000-40A>=67000

Simplifying, you get 20A>=19000,

Thus, A>=950, meaning you have to sell at least 950 adult tickets to cover production costs.

To check, substitute A = 949 in (2), meaning C = 251

60(949)+40(251) = 56940+10040 = 66980, which is just under the 67,000 worth of production costs. Thus, our answer is correct

Hope this helps

Answer 4

Hi,
I am not sure asto what is Split point method but here is a way to solve the above.

Let x be the no of adults that have to be seated.
Hence the no of children will be (1200 - x)

Hence , the total sum must be 67,000
The sum due to adults is 60x.
The sum due to children is 40(1200 - x).

The total = 67,000 = 60x + 40(1200 - x)
67000 = 60x + 48000 - 40x
=> 20x = 19000
=> x = 950

So, the no of adults must be greater than 950
and the no of children must be less than 250.

Peace out.

Answer 5

Let x be the no. of adults
and y the no. of children.
The equations for this problem are
x+y=1200
60x+40y=67000
y=1200-x
60x+40[1200-x]=67000
20x=19000
x=950
y=250
verify
950*60+250*40
=57000+10000
=67000
ok

Answer 6

You need two equations to solve.

x+y=1200
60x+40y=67,000

eliminate the Y's by multiplying the first equation by -40 and the second by 1.

(-40)x+y=1200 -40x-40y=-48000 20x=19000
(1)60x+40y=67000 60x+40y=67000 x=950

Answer 7

Minimum amount of adult seats assuming no children turn up is 67000/60= 1116.6 or 1117 seats. then we don't need to consider children.

Answer 8

Give the Points to Pradyumna N.


Good luck!