Rebecca has 45 coins, all nickels and dimes. the total value of the coins is $3.60. how many
of each type of coin does rebecca have?

Rebecca has 18 nickels and 27 dimes

Step-by-step explanation:

Let x be the number of nickels Rebecca has, then 45-x is the number of dimes she has.

The total value of Rebecca's coins is $3.60.

1 nickel - 5 cents

x nickels - 5x cents

1 dime - 10 cents

45-x dimes - 10(45-x) cents

Total x nickels and 45-x dimes is 5x+10(45-x) cents that is $3.60=360 cents. So,

5x+10(45-x)=360

5x+450-10x=360

5x-10x=360-450

-5x=-90

5x=90

x=18

45-x=45-18=27

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 ☺