Question

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?

Answer 1

Kid tickets = $4

Adult tickets = $7

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!