Question

I’M LOSING TIME!!!!!!

you are trying to decide which cell phone plan to purchase. Plan A chargeres $40 for a new phone and $20 a month for usage. Plan B provides the phone for free, but has a fee of $30 a month for usage.
Use the substitution method to determine when the two plans will cost the same.

Answer 1

Answer:

In 4 months the two plans will cost the same.

Step-by-step explanation:

Let $x$ represent the number of months of usage of phone

Let $y$ represent the total amount charged by the plans.

Plan A:

Plan A charges $40 for a new phone and $20 for per month usage.

Fixed charge = $40

Per month usage charge = $20

Usage charges in dollars for $x$ months will be = $20x$

Thus total charges $y$ in dollars can be given as:

A) $y=20x+40$

Plan B.

Plan B provides the phone for free, but has a fee of $30 for per month usage.

Fixed charge = $0

Per month usage charge = $30

Usage charges in dollars for $x$ months will be = $30x$

Thus total charges $y$ in dollars can be given as:

B) $y=30x$

In order to determine the number of month in which the two plans will charge same we will equate the equations.

Substituting equation B in equation A.

$30x=20x+40$

Solving for $x$

Subtracting both sides by $20x$

$30x-20x=20x-20x+40$

$10x=40$

Dividing both sides by 10.

$\frac{10x}{10}=\frac{40}{10}$

∴ $x=4$

Thus, in 4 months the plans will cost the same.