At the beginning of 2010, City A had a population of 2,425 and was growing by 27 residents per year. City B had a population of 1,813 and was growing by 63 residents per year. If this trend continues in what year will the populations of the two cities be the same?

17 years

Step-by-step explanation:

City A is currently 2,425 people in number and growing at 27 per year.

An expression to find the population in a given year assuming the year is x would be:

= 2,425 + 27 * x

= 2,425 + 27x

Applying the same logic to City B would give an expression of:

= 1,813 + 63x

Equating these together will give the year they will be the same:

2,425 + 27x = 1,813 + 63x

2,425 - 1,813 = 63x - 27x

612 = 36x

x = 612/36

x = 17 years

c) yes, because of asa or aas

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 ☺