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

In 4 months the two plans will cost the same.

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.

`(10x)/(10)=(40)/(10)`

∴
`x=4`

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