Question

You to rent a company A charges $25 per week plus a one-time fee of $52 Company b charges 37 per week plus a one time fee of $16. Ater how many weeks are the total casts the same at both companies

Answer 1

Question:

You to rent a company A charges $25 per week plus a one-time fee of $52 Company b charges 37 per week plus a one-time fee of $16. After how many weeks are the total casts the same at both companies​.

Solution:

Let's denote by w the number of weeks. Now, notice that for company A we have the following linear equation:

$25w+52$

and for company B, we have the following linear equation:

$37w+16$

then, to find after how many weeks are the total casts the same at both companies​, we must equal the two previous equations and solve for w:

$25w+52\text{ = 37w+16}$

this is equivalent to:

$37w-25w\text{ = 52-16}$

this is equivalent to:

$12w\text{ = 36}$

then, solving for w we get:

$w\text{ = }\frac{36}{12}\text{ = 3}$

Then. we can conclude that the correct answer is:

after 3 weeks.