Arnold's Mail Manufacturing is a company that produces chain mail. Their most popular product is saw-cut metal links that hobbyists can use to make their own creations. The company recently spent $40 on advertising, which they hope to make back quickly. The wire used to produce one gram of links costs $2, but the finished links sell for $4 per gram. Eventually, the company will make back its investment and break even. What will their expenses and sales both equal? Write a system of equations, graph, and state the solution in a complete sentence.

The System of equations :

Their expenses and sales both equal at selling 20 grams of links.

Step-by-step explanation:

Company spent on advertising = $40

Cost of production of 1 gram of links = $2

Let x be the no. grams of links produced by company

So, cost of production of x grams of links = 2x

So, Total cost of production of x grams of links=40+2x

Selling price of 1 gram of links = $4

Selling price of x grams of links = 4x

We are supposed to find What will their expenses and sales both equal.

So,

So, Their expenses and sales both equal at selling 20 grams of links.

System of equations:

Refer the attached graph

--- Blue line

--- Green line

Hence The System of equations :

and Their expenses and sales both equal at selling 20 grams of links.

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 ☺