The members of a band are arranged in a rectangular formation. When they are arranged in 8 rows, there are 2 positions unoccupied in the formation. When they are arranged in 9 rows, there are 3 positions unoccupied. How many members are in the band if the membership is between 100 and 200

150

Step-by-step explanation:

Using 8 rows leaves  2 positions unoccupied implies that the population of the number  of members in the band is 2 less than a  multiple of 8. That makes this an even  number.

Similarly, we understand that the number  of members is 3 less than a multiple of  9. So, If we list the even numbers  that are 3 less than multiples of 9  between 100 and 200 and are even; we have:

117 – 3, 135 – 3, 153 – 3, 171 – 3,  189 – 3

= 114, 132, 150, 168, 186  

Also, the numbers that are two less than  a multiple of 8:  

102, 110, 118, 126, 134, 142, 150, 158,  166, 174, 182, 190, 198

From above, we will realize that the number common in both is 150

Let's check if that satisfy our calculation;

SO:

150/8 = 18 remainder 6 ; Thus 8 - 6 = 2 (positions)

150/9 =  16 reminder 6 ;  Thus  9 - 6 = 3 (positions)

Hence the number of members in the band if the membership is between 100 and 200 is 150

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 ☺

- (2, -7)

- lines r and s and lines t and u must be parallel