Steven and Jennifer meet their friends at the movies and buys them popcorn and drinks. Steven spends $138.50 for 12 drinks and 5 bags of popcorn. Jennifer buys two drinks and seven bags of popcorn for a total of $57. How much was each drink and each bag of popcorn?

The cost of each drink was $9.25 and the cost of each popcorn was $5.5

Step-by-step explanation:

Let the cost of each drink be d

Let the cost of each popcorn be p

Steven spends $138.50 for 12 drinks and 5 bags of popcorn. This implies that:

12d + 5p = 138.50 (1)

Jennifer buys two drinks and seven bags of popcorn for a total of $57. This implies that:

2d + 7p = 57 (2)

We have two simultaneous equations/

12d + 5p = 138.50 (1)

2d + 7p = 57 (2)

Multiply (2) by 6 and subtract (1) from it:

12d + 42p = 342

- 12d + 5p = 138.50

———————————

37p = 203.5

p = $5.5

Puutting the value of p back in (2):

2d + 7(5.5) = 57

2d + 38.5 = 57

2d = 57 - 38.5 = 18.5

d = 18.5 / 2 = $9.25

The cost of each drink was $9.25 and the cost of each popcorn was $5.5

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