Question

A cable TV provider $A$, charges each customer $\$120$ for installation, plus $\$25$ per month for cable programming. It's competitor ,$B$, charges each customer $\$60$ for installation, plus $\$35$ per month for cable programming. Find the number of months for which a customer who signs up with cable provider $A$ pays so that he will pay the same total amount for cable TV as a customer who signs up with cable provider $B$ after the same number of months.

• A. $3$
• B. $6$
• C. $10$
• D. $18$

Answer 1

Answer: (B)

$6$

Now, since the problems asks you to find out how many months ($x$) would make the two amounts the same, you set the equations equal to each other. You would have
$25x+120=35x+60$
Then subtract $25x$ from both sides to get:
$120=10x+60$
Then subtract $60$ from both sides to get:
$60=10x$ or
$10x=60$ (same thing)
Divide both sides by $10$ to get:
$x=6$
Therefore, two people would need to sign up for $6$ months at the different companies to pay the same amount of money.