Amovie theater charges $6.50 for morning tickets and $8.75 for night tickets the theater sold 378 tickets for a total amount of $2929.50 how many morning tickets were sold

The number of sold morning tickets are 168.

Step-by-step explanation:

Given,

Total number of tickets = 378

Total earned amount = $2929.50

Charge of each morning ticket = $6.50

Charge of each night ticket = $8.75

Solution,

Let the number of morning tickets be 'x'.

And also let the number of night tickets be 'y'.

So, the total number of tickets is the sum of number of morning tickets and number of evening tickets.

So, framing in equation form, we get;

Again, Total earned amount is the sum of number of morning tickets multiplied with charge of each ticket and number of evening tickets multiplied with charge of each ticket.

So, framing in equation form, we get;

On multiplying equation 2 by 100 on both side, we get;

Now multiplying equation 1 by '650', we get;

Now subtracting equation 4 from equation 3, we get;

Now substituting the value of'y' in equation 1, we get;

Hence The number of sold morning tickets are 168.

Whereas The number of sold night tickets are 210.

pooopoopopoopop

step-by-step explanati∵∵∴∴on:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12