Question

Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $75. For one performance, 15 advanced tickets and 20 same-day tickets were sold. The total amount paid for the tickets was $1300. What was the price of each kind of ticket?

Answer 1

Hi @moon1619

Answer 2

Do you know how to come up with the equations to solve this question?

Answer 3

@AZ kind of I struggle with math is it 75x+15=1300?

Answer 4

That's alright! And unfortunately it isn't

We need to come up with TWO separate equations and then solve it

Answer 5

So we have two different type of tickets

an advance ticket
and a same-day ticket

do you want to choose a letter (or variable) for it?
we can stick with x or y, unless you want to use something else like A for advance ticket and S for same-day ticket

Answer 6

So

X + Y = $75

Once you find the (X) or the advanced and the (Y) or the same day you multiply (X) by (15) and (Y) by (20)

Answer 7

@AZ I use X and Y

Answer 8

@AZ @cripQUEZZ would the first one be 15x+20y=1300

Answer 9

Well first we gotta find wat x and y equal

Answer 10

obv

Answer 11

That's correct!

Answer 12

And like @CripQUEZZ already said, the other equation would be x + y = 75

Answer 13

Yeah

Answer 14

so x is our advanced tickets
y is our same-day tickets

Answer 15

So do you know how to solve a system of equations?

There's three methods
1. Elimination method
2. Substitution method
3. Graphing

Answer 16

Are you familiar with any of these?

Answer 17

@AZ yes

Answer 18

Which one would you like to use?

If you already know how to do the substitution and elimination method and you're just trying to solve it faster, the graphing method is the fastest way
and we can use
https://www.desmos.com/calculator

Answer 19

So your two equations are

15x + 20y = 1300

And

X + Y = 75

Answer 20

Do the first equation then you can get he second one easily

Answer 21

The point where the two lines intersect would be the solution to the two equatons
the x-value giving you the price for advanced tickets
and the y-value giving you the price for same-day tickets

Answer 22

@AZ so if I graph 15 and 20 whatever the intercept is is the answer?

Answer 23

You graph the two lines

x+y=75
15x+20y=1300

Where the two lines intersects gives you the answer.

The intercepts are different than where they INTERSECT (different words)

Answer 24

But only use this graphing method if you're comfortable with solving the system of equations by either the substitution or elimination method
It's important to know how to do it by yourself first :)

Answer 25

@AZ oh ok I don’t understand how to graph it but to solve this would I do 15x+20y=1300 subtract 20 from 1300 then divided by 15

Answer 26

(also you don't have to @ me in every message since I get a notification each time you respond)

Answer 27

we can't subtract 20 because there's a 'y' with it

we have to solve the two equations together

Answer 28

No not really youll divide both numbers

Answer 29

so let's do it step by step

first we have

x + y = 75

can you solve this for x?

Answer 30

(Oh ok) yes but we have to rearrange it so X would equal 75 I think

Answer 31

no no no

think of x as apples and y as bananas

you can't just throw away the bananas and say that there are 75 apples

Answer 32

So then we can’t solve for X so we move to 15x+20y=1300

Answer 33

x + y = 75

we have two DIFFERENT letters here

to get 'x' all by itself, we have to subtract y on both sides

and we get

x + y - y = 75 - y

banana minus banana = no banana
so on the left hand side of the equal sign, the `y` gets cancelled out
and on the right hand side, we keep the y

and so we're left with

x = 75 - y

Answer 34

does that make sense?

Answer 35

Yes

Answer 36

so now we can use the substitution method and we'll plug that into the other equation

let me add some colors for you

Answer 37

\(\color{orange}{x} = \color{orange}{75-y}\)

\( 15\color{orange}{x}+20y=1300\)

so we can replace the `x` in the second equation with `75-y` from the first equation because
we said that x = 75 - y
so 75-y is the same thing as x so we can replace it

this is called the substitution method

Answer 38

still following along or do you have any questions?

Answer 39

\(\color{#0cbb34}{\text{Originally Posted by}}\) @AZ
\(\color{orange}{x} = \color{orange}{75-y}\)

\( 15\color{orange}{x}+20y=1300\)

so we can replace the `x` in the second equation with `75-y` from the first equation because
we said that x = 75 - y
so 75-y is the same thing as x so we can replace it

this is called the substitution method
\(\color{#0cbb34}{\text{End of Quote}}\)
very very good job !!!

Answer 40

I kind of understand that but still confused because now the X isn’t there

Answer 41

so we can use ANY letter

we can use A or B or X or Y

and these are just variables

just imagine that y as your NEW `x`
and you just solve for `y` as you would solve for `x`

Answer 42

Does that help?

Answer 43

So would it be 15 (75-y)+20y=1300

Answer 44

You got it!

now just solve for `y`

Answer 45

Y= 35 and x=40

Answer 46

Great job!!

Answer 47

The only thing is I don’t know what x represents and what y represents

Answer 48

Would x be the advance tickets?

Answer 49

\(\color{#0cbb34}{\text{Originally Posted by}}\) @AZ
so x is our advanced tickets
y is our same-day tickets
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 50

Ok thank you so much

Answer 51

Yes! Because as you noticed in our equation

15x+20y=1300

we're multiply 15 with x
and 15 was how many advanced tickets they bought
x is going to be `the price of each advanced ticket`

and similarly
y will be the `price of each same-day ticket`

Answer 52

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Moon1619
Ok thank you so much
\(\color{#0cbb34}{\text{End of Quote}}\)

You're most welcome!