Three roommates Ava, Ben, and Cora went grocery shopping online. Ava spent three times as much as Ben and half as much as Cora. If together they spent a total of 50, how much did Cora spend?

Cora spent $ 30

Step-by-step explanation:

1. This is the information given to us to answer the question correctly:

x = Amount of money Ben spent

3x = Amount of money Ava spent (Ava spent three times as much as Ben)

6x = Amount of money Cora spent (half as much as Cora)

2. If together they spent a total of 50, how much did Cora spend?

Let's solve for x, this way:

x + 3x + 6x = 50

10x = 50

x = 50/10

x = 5

In consequence,

Ben spent $ 5 (x)

Ava spent $ 15 (3x)

Cora spent $ 30 (6x)

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 ☺