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14. The maximum capacity for seating in a theater is 500 people. The theater sells two types of tickets, adult tickets for $7.25 each and child tickets for $4 each. If they sold out on a certain showtime and made a total of $3,157 in ticket sales, how many of each types of tickets was sold out that showtime?



Answer :

ann1104

Step-by-step explanation:

set x as the number of the adults in the show

500-x - number of children

(500-x)×4+7.25x=3157

2000-4x+7.25x=3157

3.25x=1157

3×1/4x=1157

13/4x=1157/×4

13x=4628/÷13

x=356

356 adult tickets was sold out.

500-356=144

144 child tickets was sold out.

View image ann1104
semsee45

Answer:

Adult tickets sold = 356

Child tickets sold = 144

Step-by-step explanation:

Given information:

  • Maximum number of seats = 500
  • Cost of adult ticket = $7.25
  • Cost of child ticket = $4
  • Total revenue of sold-out show = $3,157

Define the variables:

  • Let x = the number of adult tickets sold.
  • Let y = the number of child tickets sold.

Create two equations from the given information:

[tex]\textsf{Equation 1}: \quad x + y = 500[/tex]

[tex]\textsf{Equation 2}: \quad 7.25x+4y=3157[/tex]

Rewrite Equation 1 to make y the subject:

[tex]\implies y=500-x[/tex]

Substitute this into Equation 2 and solve for x:

[tex]\implies 7.25x+4(500-x)=3157[/tex]

[tex]\implies 7.25x+2000-4x=3157[/tex]

[tex]\implies 3.25x+2000=3157[/tex]

[tex]\implies 3.25x=1157[/tex]

[tex]\implies x=356[/tex]

Substitute the found value of x into the rewritten form of Equation 1 and solve for y:

[tex]\implies y=500-356[/tex]

[tex]\implies y=144[/tex]

Solution

  • Adult tickets sold = 356
  • Child tickets sold = 144

Learn more about systems of equations here:

https://brainly.com/question/28281431

https://brainly.com/question/27034625

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