Aplay is performed for a crowd of 400 people. adult tickets cost $22 each, student tickets cost $15 each, and tickets for children cost $13.50 each. the revenue for the concert is $7840. there are 40 more children at the concert than students. how many of each type of ticket are sold?

280 adult tickets, 40 student tickets and 80 children tickets were sold.

Step-by-step explanation:

To solve this problem let's call:

x = number of tickets for adults

y = number of tickets for students

z = number of tickets for children

The income for the concert is $ 7840

Then we can raise the following equations according to the given conditions:

  (i)

(ii)

 There are 40 more children in the concert than students:

So:

 (iii)

We then have 3 equations and 3 unknowns:

To solve the system we multiply the equation (i) by -22 and add it to the equation (ii)

So:

       +

(iv)

 Now we multiply (iii) by 7 and add it to (iv)

   +

(v)

We substitute (v) in (iv) and we have

(vi)

We substitute (v) and (vi) into (i) and we have:

280 adult tickets, 40 student tickets and 80 children tickets were sold.

answer:

c) the x-coordinate of the center of the circle increases by 3