This is a word problem?

Question

Tickets for the community theater cost $12 for adults and $8 for a child. If 130 tickets were sold and totals $1160, how many of each type of ticket were sold?

Answer 1

let

x = Child

y = adult

130 = total tickets sold

8 = child ticket cost

12 = adult ticket cost

1160 = total money collected

- - - - - - - - -

x + y = 130- - - - - - - -Equation 1
8x + 12y = 1160- - - -Equation 2
- - - - - - - - - - - -

Substitute method 1

x + y = 130

x + y - x = - x + 130

y = - x + 130

substitute the y value into equation 2

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

8x + 12y = 1160

8x + 12( - x + 130) = 1160

8x + (- 12x + 1560) = 1160

8x - 12x + 1560 = 1160

- 4x + 1560 = 1160

- 4x + 1560 - 1560 = 1160 - 1560

- 4x = - 400

- 4x / - 4 = - 400 / - 4

x = - 400 / - 4

x = 100

Insert the x vallue into euation 1

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

x + y = 130

100 + y = 130

100 + y - 100 = 130 - 100

y = 30

Insert the y value into equation 1

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

Check for equation 1

x + y = 130

100 + 30 = 130

130 = 130

- - - - - - - - --

Check for equation 2

8x + 12y = 1150

8(100) + 12(30) = 1160

800 + 360 = 1160

1160 = 1160

- - - - - - - - - - -

There were 100 child tickets sold and 30 adults tickets sold

- - - - - - - -

Both equations balance

The solutio set { 100, 30 }

- - - - - - - -s-

Answer 2

Let a=adults and c=children tickets
a + c = 130 => a = 130 - c
12a + 8c = 1160
=> 12 (130-c) +8c = 1160
=> c = 100
=> a = 30

Answer 3

Let A be the number of adult tickets and C be the number of child.
A+C = 130.
12A + 8C = 1160.

Substitution method is the easiest way to solve this (put A=130-C into the second equation, get C=100, so A=30.

100 Child tickets and 30 Adult.

Answer 4

this problem is under system linear equation of two unknowns
let x - no. of adults
y - child
the equations are
x+y=130 - as equation 1
12x+8y = 1160 as equation 2
using elimination by subtraction, multiply equation 1 by 8
results in
8x+8y = 1040 as new equation
subtract the new equation from equation 2
results in
4x = 120 therefore
x = 30 tickets for adults
and y = 130 - 30 = 100 ticket for child
summary of answers:
x = 30 tickets for adult
y = 100 tickets for child

Answer 5

let x tickets of adults and y of children

we can form two eqs as follows 12x+8y =1160
x+y =130
therefore x=30 ,y=100

Answer 6

Hint: let 'a' be the number of adult tix and 'c' be the number of child tix.

Write two equations:

1. #adults + #children = total num of people

2. $12 times #adults + $8 times #children = total $ amt

The rest of your HW is left for you to solve :)

Answer 7

yes