To raise money to attend boy scout camp, alec is selling popcorn. small bags of popcorn sell for $4 each and large bags sell for $6 each. he needs to earn at least $300 to attend camp. he will also earn a badge if he sells at least 60 bags total of any combination. write a system of linear inequalities to represent this situation, then graph

Let's assume

number of small bags of popcorn =x

number of large bags of popcorn =y

He will also earn a badge if he sells at least 60 bags total of any combination

so, we get

Small bags of popcorn sell for $4 each

so, total price of small bags of popcorn =4x

large bags sell for $6 each

so, total price of large bags of popcorn =6x

He needs to earn at least $300 to attend camp

so, we get

we know that quantities can never be negative

so, we get

so, we get system of inequalities as

Graph:

step-by-step explanation:

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 ☺