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.

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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.

Answer :

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wifilethbridge wifilethbridge · Answer 1 · 2025-03-30T01:22:32-04:00

Answer:

The System of equations :

[tex]40+2x=y \\4x=y[/tex]

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, [tex]40+2x=4x[/tex]

[tex]\Rightarrow 40=2x\\\Rightarrow \frac{40}{2}=x\\\Rightarrow 20=x[/tex]

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

System of equations:

[tex]40+2x=y\\4x=y[/tex]

Refer the attached graph

[tex]40+2x=y[/tex] --- Blue line

[tex]4x=y[/tex]--- Green line

Hence The System of equations :

[tex]40+2x=y \\4x=y[/tex]

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