Please show an explanation

Step-by-step explanation:

1) Let x be the number of adults and y be the number of students

x + y = 8 (I)

        y = 8 -x

7.25x + 5.50y = 52.75 (II)

Substitute y = 8 -x in equation (II)

7.25x + 5.5*(8 - x) = 52.75

7.25x + 5.5*8 - x*5.5 = 52.75

7.25x +  44 - 5.5x = 52.75

7.25x - 5.5x + 44 = 52.75

             1.75x + 44 = 52.75

                  1.75x    = 52.75 - 44

                       1.75x = 8.75

                           x = 8.75/1.75

x = 5

Plugin x = 5 in equation 1

y = 8 - 5

y = 3

2)  x = y + 24

x + y = 180   {Supplementary}

y + 24 + y = 180

2y + 24 = 180

      2y = 180 - 24

     2y =  156

        y = 156/2

y = 78

x = 78 + 24 = 102

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺