Answered

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
Logan wrote a business plan for an entrepreneurship class, and now he has to make bound copies. Logan could use a printer who charges a setup fee of $42 and $4 for every copy printed. Another possibility is to go to the office supply store, where he could pay an up-front fee of $30 and $8 per copy. There is a certain number of copies that makes the two options equivalent in terms of cost. How many copies is that? How much would the copies cost?
For ____copies, the cost is $____

Answer :

musiclover10045

Set up two equations:

Printer: 42 + 4C

Supply Store: 30 + 8C

C = number of copies.

Now set them equal to each other and solve for C.

42 + 4C = 30 + 8C

Subtract 4C from each side:

42 = 30 + 4C

Subtract 30 from each side:

12 = 4C

Divide each side by 4:

C = 12/4

C = 3

For 3 copies, the cost is $54

System of equations helps to compare two situations. The number of copies that make the two options equivalent in terms of cost is 3.

What is a system of equations?

The system of equations helps us to compare two real-life problems, such that it tells us which one of the two options must be done in order to maximize the output.

Given to us

Printer 1 - charges a setup fee of $42 and $4 for every copy printed.

Printer 2 - charges a setup fee of $30 and $8 for every copy printed.

For printer1 we know that, the setup cost is $42 therefore, even if Logan makes no copy he needs to pay $42, while he needs to pay $4 for x number of copies, therefore, the total cost of Printer1 can be written as,

y = 42 + 4x

For printer2 we know that the setup cost is $30 therefore, even if Logan makes no copy he needs to pay $30, while he needs to pay $8 for x number of copies, therefore, the total cost of Printer2 can be written as,

y = 30 + 8x

Finding the solution of the two equations we will get the number of copies(x), that is needed to be done in order to make the two options equivalent,

The value of y is already known to substitute the values opposite to each other,

[tex]y = y\\\\42 + 4x = 30 +8x\\\\42 - 30 = 8x-4x\\\\12 = 4x\\\\x = 3[/tex]

Hence, the number of copies that make the two options equivalent in terms of cost is 3.

Learn more about System of equations:

https://brainly.com/question/12895249

${teks-lihat-gambar} ap8997154

Other Questions