Question

1. A local movie theater charges $12 for an adult ticket and $10 for a child’s ticket. A group of
eight people spent a total of $86 on tickets to a movie. How many adults and how many
children were in the group?
a. Write a system of linear equations based on the description. Use x to represent the
number of adults and y to represent the number of children.

Answer 1

Well we know that they spent a total of 86 on tickets.

12 each for adults
10 each for children's

so we have

12a + 10c = 86

*sorry letting x = adults and y = childrens

12x + 10y = 86

Answer 2

ok thank you i just wanted to make sure my equation was right

Answer 3

Also have the other equation to do ...

there were 8 total people so

x + y = 8

Answer 4

i have another question to if you would like to help?

Answer 5

its the same problem to

Answer 6

yeah no problem

Answer 7

Solve the system using the elimination method. Show all the steps leading to your
answer

Answer 8

Oh, so now we solve the system using elimination...okay...well we had our 2 equations

x + y = 8
12x + 10y = 86

We want to eliminate a variable...lets eliminate 'y'

multiply that top equation by -10

-10x - 10y = -80
12x + 10y = 86

Now when we ADD the equations together...the -10y and +10y cancel out..so we have

-10x + 12x = ...?
-80 + 86 = ...?

Answer 9

We add the top and bottom equations together?

Answer 10

Yes that is how the elimination method works...you make it so the 2 equations "when added together" get rid of 1 variable..making it possible to solve for the other variable

Answer 11

-90 +98 =8 ? I dont know I'm not that smart when it comes to this.

Answer 12

Don't worry about it

so when we have the 2 equations

x + y = 8
12x + 10y = 86


We want to multiply the top equation...by some number to eliminate one of the variables...I chose to eliminate 'y'

to get rid of 10y...we need to have a -10y..because -10y + 10y = 0 (canceled)

so

we multiply everything in that top equation by -10

-10x - 10y = -80

now the second equation stays the same

12x + 10y = 86


Now add them

-10x + 12x = ...?
-10y + 10y = ...?
-80 + 86 = ...?

Answer 13

Ok hold on this might take a moment

Answer 14

No problem!

Answer 15

-10x + 12x = 2

-10y + 10y = 0

-80 + 86 = 6

Answer 16

Numbers = correct...but remember the variables stay when you add

-10x + 12x = 2x (keep the variable)

great...so now we have

2x = 6

what does 'x' equal ...?

Answer 17

3?

Answer 18

Right...x = 3

This says that you had 3 adults that went


Now we can go back to our original equations

x + y = 8

we now know 'x'... = 3....so lets find 'y'

3 + y = 8

y = ...?

Answer 19

5!

Answer 20

Right!

So we have 3 adults...and 5 children

Lets check it

We had another equation right?

12x + 10y = 86

plug in x = 3 and y = 5 and see if it works...

Answer 21

You want me to use it on that equation?.. how would i do that? 12 x 3 + 10 x 5 = 86?

Answer 22

Exactly...We already have the answer...this is just how you check it...

we know 'x' = 3 and 'y' = 5

So we replace 'x' and 'y' with those values

12x + 10y = 86
12(3) + 10(5) = 86

Answer 23

Ohhh i see so thats the answer?

Answer 24

12(3) + 10(5) = 86
36 + 50 = 86

86 = 86

So now we know for SURE that

there were 3 adults and there were 5 children

Answer 25

Ok thank you! i just need one more question to finish this problem. Write 1-2 sentences to explain what the solution means for this situation

Answer 26

So i just write down the steps right?

Answer 27

Well yeah I suppose...you could say....the solution means that there were 3 adults and 5 children that went to the movies

Something to that extent...

Answer 28

Ok thank you for the help. i appreciate it man. I really needed to get this assignment done and you made it really simple.

Answer 29

No problem!