Question

Suppose that you have $114 for tickets, and you want 6 tickets in the upper box section for weekday and weekend games. A ticket for the weekday is $18 and the weekend is $21. How many of each ticket can you buy?

Answer 1

I got the answer, x=4 y=2, but I don't know how to show my work

Answer 2

Let x = number of $18 ticket
Let y = number of $21 ticket

x + y = 6
the total number of tickets is 6

18x + 21y = 114
18x is the cost of x $18-tickets;
21y is the cost of y $21-tickets;
18x + 21y is the total spent = 114

x + y = 6
18x + 21y = 114

Solve the system of equations.

Answer 3

y=2 x=4

Answer 4

You already had written you knew the answer. Do you know how to solve the system of equations, or do you need help with it?

Answer 5

I need help with solving the system of equations (showing my work)

Answer 6

I've gotten to the step 18(6-y)+21y=114... after that I am stuck

Answer 7

Ok
x + y = 6
18x + 21y = 114

Let's solve the system of equations using the substitution method.

In this method, you first solve one equation for one variable.
Oh, I see, you're getting there.
x = 6 - y
18(6 - y) + 21y = 114
This is exactly what you have so far.

Answer 8

Now distribute the 18

Answer 9

108-18y+21y=114

Answer 10

18(6) - 18(y) + 21y = 114

Answer 11

Right

Answer 12

Now combine like terms on the left side

Answer 13

108-39y=114 ?

Answer 14

Careful with that addition.
-18y + 21y
You are adding two quantities with different signs, -18y and 21y

Answer 15

ohhhhhhh okkk! Thank you for catching that!!! 108+3y=114

Answer 16

and then -108 from both sides ???

Answer 17

3y=6/3 y=2!

Answer 18

The rule is take absolute values of the numbers:
|21| = 21
|-18| = 18
Then subtract the smaller one from the larger one:
21 - 18 = 3
Then the sign is the same sign as the number that has the larger absolute value.
21 has a larger abs value than -18, and 21 is positive, so the answer is positive.
so -18 + 21 = +3

Answer 19

Thanks!

Answer 20

3y = 6
y = 2.
Correct. Now substitute y = 2 into one of the original equations to get x.

Answer 21

x=4

Answer 22

x + 2 = 6
x = 4
Correct.

Answer is: 4 $18 tickets and 2 $21 tickets.

Notice there is no x and y in the answer above. That is because the question does not use any x and y. We used x and y to represent the question mathematically. The person asking the question wants to know the numbers of tickets and has no idea what x and y are.

Answer 23

ahh right. Your attention to detail saved me! haha thanks so much!

Answer 24

You're welcome.

Answer 25

What grade are you in? (math student)