At a movie theatre, the price of 2 adult tickets and 4 child tickets is $48. the price of 5 adult tickets and 2 child tickets is $64. what is the price for one child and one adult ticket.
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The ticket for an adult costs $10 and the ticket for a child costs $7

Based on the information given, the equation to solve the question will be:

2a + 4c = 48

5a + 2c = 64

Multiply equation i by 5

Multiply equation ii by 2

10a + 20c = 240

10a + 4c = 128

Subtract the equations

16c = 112

c = 112/16

c = 7

The ticket for a child is $7

Since 2a + 4c = 48

2a + 4(7) = 48

2a + 28 = 48

2a = 48 - 28

2a = 20

a = 20/2

a = 10

The ticket for an adult cost $10

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The price for one adult is $10 while the price for one child is $7

Step-by-step explanation:

Let

price for an adult = a

price for a child = b

2a + 4b = 48(i)

5a + 2b = 64(ii)

make a subject of the formula in equation (i)

2a = 48 - 4b

divide through by 2

a = 24 - 2b

Insert the value of a in equation (ii)

5(24 - 2b) + 2b = 64

120  - 10b + 2b = 64

collect like terms

- 8b = 64 - 120

-8b = -56

divide both sides by -8

b = 7

insert the value of b in equation(i)

2a + 4(7) = 48

2a + 28 = 48

2a = 48 - 28

2a = 20

divide both sides by 2

a = 10

The price for one adult is $10 while the price for one child is $7

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204