Adult tickets for a play cost $15 and child tickets cost $11. If there were 23 people at a performance and th

Question

Adult tickets for a play cost $15 and child tickets cost $11. If there were 23 people at a performance and the theater collected $309 from ticket sales, how many children attended the play?
a) 8
b) 9
c) 10
d) 14

Answer 1

15x + 11y = 309
x + y = 23
15x + 15y = 15*23

Eliminate x to get
4y = 15*23 - 309
y = 9
answer b

Answer 2

Substitution Method

let

x = children

y = adults

23 = total children and adults

11x = cost of children tickets

15 = cost of adults tickets

309 = total collected

- - - - - - - - - - -

x + y = 23- - - - - - - - - -Equation 1
11x + 15y = 309- - - - -Equation 2
- - - - - - - - - - - -

x + y = 23

x + y - x = - x + 23

y = - x + 23

Substitute the y value into equation 2

- - - - - - - - - - - -

11x + 15y = 309

11x + 15(- x + 23) = 309

11x +(- 15x + 345) = 309

11x - 15x + 345 = 309

- 4x + 345 = 309

- 4x + 345 - 345 = 309 - 345

- 4x = - 36

- 4x/-4 = - 36/-4

x = - 36/-4

x = 9. . . .Number of Children

Insert the x value into equation 1

- - - - - - - - -

x + y = 23

9 + y = 23

9 + y = 9 = 23 - 9

y = 14. . . .Number of adults

Insert the y value into equation 1

- - - - - - - - - -

Check for equation 1

x + y = 23

9 + 14 = 23

23 = 23

- - - - - - - - -

Check for equation 2

11x + 15y = 309

11(9) + 15(14) = 309

99 + 210 = 309

309 = 309

- - - - - - - - - -

Both equations balance

The solution set { 9, 14 }

- - - - - - - - - - -s-

Answer 3

First set up equation, adults equal x and children equal y.
So:
X+Y=23 people at performance
15X+11Y=309 dollars collected.
Use substitution for this one, so -
Y=23-X
So where ever you see Y in the second equation, put in 23-X -
15X+11(23-X)=309 or 15X+253-11X=309
Combine like terms -
4X=56
Divide by 4 on each side
X=14
Plug in X for the first equation -
14+Y=23
Subtract 14 from each side
Y=23-14
There were 9 children at the play. Your answer is B.

Answer 4

14 Adults and 9 Children

you form the equation
15(x)+11(23-x)=309 then solve

Answer 5

let X be number of adults
let Y be number of childs

cost of adult tickets is 15$ so total value = 15X
cost of child tickets is 11$ so total value = 11Y

Total theater collection will be 15X+11Y = 309
Total people who attended is X+Y = 23

15X+15Y = 345 (multiply by 15 the equation (x+y=23))
15X + 11Y = 309
- - - (subtract the two equation/elimination method)
------------------------
4Y = 36
Y = 36/4 = 9
9 children attended the theatre (ANSWER)

Answer 6

Adults (A) and Children (C) total 20 people attending the performance. In equation this is A + C = 20 A cost is 17 C cost is 5. 17A + 5C = 280. Using substitution A = 20 - C. So 17(20 - C) + 5C = 280. This is 340 - 17C + 5C = 280. This in turn is 60 = 12C so C = 5. Therefore 15 adults and 5 children attended the play.

Answer 7

let there be a adults and c children

15a + 11c = 309

cost of adult times no of adults + cost of child times no of children = 309

a + c = 23

total no people = 23

a = 23-c

substitute

15(23-c) + 11c = 309

345 - 15c + 11c = 309

36 = 4c

c = 9

substitute in a + c = 23

a = 23 - 9

a = 14

14 adults and 9 children attended

Answer 8

let x b the no of adults and y be the children
x + y = 23
15x + 11y = 309
solving the second eq using first eq i.e. x = 23-y
y = 9
and x = 23-9 = 14

Answer 9

b) 9
A= adult tickets B= child tickets

15A + 11C= 309
A+C =23

A=23-C
15(23-C) +11C=309
solve and C= 9

Answer 10

let the number of adults be a, and the number of children be c.

Then, from the question,
$15a + $11c = $309

and, the total number of people, a+c = 23
then, a= 23-c. Replacing a,

15(23-c) + 11c = 309
345 - 4c = 309
4c = 36
c=9

therefore the answer is b) 9 children.