Ariana Grande is coming to North Gulfport Middle School for a fundraising benefit concert! Nevaeh is selling tickets. This week, she sold 3 kids tickets and 9 adult tickets for a total of $75. Last week, she sold 8 kids tickets and 5 adult tickets for $67. How much was each adult ticket, and how much was each kids ticket?

Kid tickets = $4

Adult tickets = $7

Step-by-step explanation:

3K+9A=75 this is the equation for this week, it shows how many adult and kid tickets were added up to a total of $75

8K+5A=67 this is the equation for last week, it shows how many adult and kid tickets were added up to a total of $67

here, we can use substitution or elimination with these two formulas:

3K+9A=75

8K+5A=67

Substitution method; solve one equation for a variable and use the value in the other equation, such as follows:

3K+9A=75 we will solve for the variable, K, seeing that both 9 and 75 are divisible by K's coefficient of 3

3K+9A=75 subtract 9A from both sides to get 3K=75-9A

3K=75-9A divide by 3 to get K by itself, leaving us with K=25-3A

now that we know K=25-3A, we can substitute it's new value in the other equation: 8K+5A=67

8(25-3A)+5A=67 we will multiply out to get rid of the parentheses first because of PEMDAS

200-24A+54=67 now we add like terms to simplify to 200-19A=67

now we subtract 200 from both sides to get -19A=-133

now we divide by -19 to get A by itself A=7

Now that we have A, we can plug it into any equation to get K

let's use the first equation: 3K+9A=75

3K+9(7)=75 this simplifies to 3K+63=75 and then 3K=12 we divide by 3 to get K=4

With this information, we know now that each Kid ticket cost $4 and each adult ticket cost $7

Now, if we were to use elimination, it would look like this because we eliminate one variable like I do here:

our Greatest Common Factor (GCF) is 24 between the Ks

3K+9A=75 we can multiply this whole equation by 8

8K+5A=67 and this equation by -3

8(3K+9A=75)   =   24K+72A=600

-3(8K+5A=67)  =  -24K-15A=-201

if we set this up like subtraction, we can eliminate K because 24 is cancelled out by -24 and we are left with this:

72A=600

-15A=-201

we add the equations to get this:

57A=399 and now we divide to get A

A=7

Again, now that we have A, we use it in an equation, just like in Substitution. This time I will demonstrate with the second equation: 8K+5A=67

8K+5(7)=67 ypu should know the steps by now, so I am going to skip to the last step:

8K=32 K=4

Hope that helps!

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

ιт ωαѕ 5¢м вє¢αυѕє 1/4 σf 20 ιѕ 5

αи∂ 5*4=20

нσρє ι ¢συℓ∂ нєℓρ уσυ