Question

Two families go to a hockey game. One family purchases two adult tickets and four youth tickets for $28. Another family purchases four adult tickets and five youth tickets for $45.50. Let x represent the cost in dollars of one adult ticket and let y represent the cost in dollars of one youth ticket.

Write and solve a linear system of equations to find the cost of one adult and one youth ticket.

Answer 1

Hey there! Welcome to QuestionCove!

Do you have any idea how to come up with the equations we will eventually solve?

Answer 2

Hi, I only needed to put this up here to see if I could get the equation itself.

Answer 3

Probably asking for too much :/

Answer 4

Sure!

Not at all!

Answer 5

We have two families

One family purchases 2 adult tickets and 4 youth tickets for $28

The other family purchases 4 adult tickets and 5 youth tickets for $45.50

x is the cost of 1 adult ticket
y is the cost of 1 youth ticket

Answer 6

(That's basically the question just made easier to read to separate all the information haha)

Answer 7

Okay! Anything that helps is great! Thank you!

Answer 8

Let's focus on the first family

So we said that `x` is how much 1 adult ticket costs

If the first family bought 2 adult tickets, how much would that cost?

As an example:
I say that one watermelon costs 5 dollars
and I buy 4 of them
then how much did 4 watermelons cost?
It's a simple multiplication 5*4 = 20

So here we have an `x`
x is just our variable, it's a number that we're trying to eventually solve for

so how much would 2 adult tickets cost if each adult ticket costs `x` dollars?

Answer 9

x*2?

Answer 10

Exactly! Or 2x

Now the same thing for the youth

1 youth ticket costs `y` dollars
and the first family bought 4 of them

how much do 4 youth tickets cost?

Answer 11

4*y

Answer 12

(x*2) + (4+y)??

Answer 13

Exactly!

Answer 14

x*2 is the same thing as 2x

we write it like that because it saves space and is easier to read but it's the same thing- 2 times x
or x times 2

same thing

Answer 15

it seems smoother in my head when i do that, sorry

Answer 16

so remember the first family bought 2 adult tickets and 4 youth tickets

and all of those tickets costed 28

so
2x + 4y = 28

Answer 17

No worries! I just wanted to make sure you understood that they were the same because when we write the equation it looks much cleaner to have 2x + 4y

than to have (x*2) + (y*4)

Answer 18

ok :)

Answer 19

Adult=7, Child=3.5 i think

Answer 20

no no, so we'll find a bunch of numbers that can work

we can chose any random number for 'x' and find a price for y that would make it 28

the way to get the actual solution lies in the other equation!!

Answer 21

Don't forget about the other family

Answer 22

ohhhhhh

Answer 23

So you know how we just made that first equation? Now we need to make a second equation

and then we solve the equations together!

The other family purchases 4 adult tickets and 5 youth tickets for $45.50

Answer 24

Can you do it on your own this time? Or do you want me to help you with setting up the equation again

Answer 25

x4 + y5

Answer 26

good! And those 4 adult tickets + the 5 youth tickets costed a total of 45.50 !

so our second equation is
4x + 5y = 45.50

Does that make sense?

Answer 27

yeah, let me plug it in

Answer 28

so we have two equations that we need to solve

2x + 4y = 28
4x + 5y = 45.50

Do you know how to solve a system of equations?

The substitution method? Elimination method?

Answer 29

I learned them a while back, barely remember. It's fine, I think I can handle myself! THanks for the help!

Answer 30

Of course! That's totally fine with me. If you get stuck, I'll still be here if you want me to help or check your answer!

Answer 31

@AZ I got it right after a bit of trial and error! Thank you!

Answer 32

Were you guessing numbers the whole time?! @ENHZ

Answer 33

I could have shown you how to solve it so you wouldn't be guessing numbers because then it gets really difficult if the price of one of the tickets is 9.53 or something

Answer 34

I just fell back on the $7 adult, $3.50 child, and ended up getting it right! @AZ

Answer 35

That's correct!

Do you know how to solve it by substitution or elimination method?

Alternatively, you could have graphed both lines and saw where they intersected- that would be your answer

Answer 36

I ended up using the substitution method

Answer 37

Ah okay, good to hear!

Also- this is a really good graphing calculator
https://www.desmos.com/calculator/d0ni9dq6d9

Answer 38

Thank you @AZ

Answer 39

You're most welcome!