Mathematics, 03.08.2019 12:30 erjalinalii

Amovie theater sells adult tickets for $13 and student tickets for $8 . tuesday, a total of 56 tickets were sold, and the total money collected was $568 . how many adult tickets and how many student tickets were sold?

Answers: 2

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Let a ault tickets and s student tickets be sold.
a+s=56
13a+8s=568

s=56-a
13a+8(56-a)=568
13a+448-8a=568
5a+448=568
5a=120
a=24
s=56-24=32

24 adult tickets and 32 student tickets are sold.

Answer from: hala201490

Your solving a linear equation for this problem the easiest method of the 3 is going to be solving by elimination:
1. The adult tickets (A) coast $13 per adult and student tickets (S) coast $8. The theater sold $568 worth of tickets. because we don't know how many of each tickets were sold we multiply the prices of adults by one variable and the price of students by another variable to add up to a total of $586 hence the equation 13a+8s=568

For the second equation you simply want to add the number of adult tickets and the number of student tickets together to get the total amount of tickets which in this case Is 56 hence the equation a+s=56
13A+8S=568
A+S=56

2. the next step would be to add the equation to solve for either A or Sby first seeing if any of the variables cancel each other out. In this case they don't so you need to multiply one of the equations to make it so one of the variables cancel out. I multiplied the second equation by -13 (I chose the second equation because it's easiest) so you and up with -13(a+b=56) and then using distributive property you and up with the equation -13a-13s=-728 so your new equation ends up as:
13A+8S=568
-13A-13s=-728

3. now you can add the equations together 13a+-13a=0 (cancel each other out) 8s+-13s=-5s and 568+-728=-160 so you and up with -5s=-160

13a+8s=568
+-13a-13s=-728
-5s=-160

4. now you want to isolate s by dividing -5 into -160 which is 32 hence s=32

s=-160÷-5=32
s=32

5. now that you have your value for s you can plug it in to either equation (I used the second because it's easiest) and then to find the value of a you have to isolate a so you subtract 32 from both sides so you get a=56-32 therefore a= 24
a+32=56
a=56-32
a=24

6.You now have both values of your variables
the theater sold 32 student tickets and 24 adult tickets

Answer from: Quest

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

Answer from: Quest

1. 3/6 or 1/22. 1/123. 1/84. 1/105. 2/12 or 1/6

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Amovie theater sells adult tickets for $13 and student tickets for $8 . tuesday, a total of 56 ticke...