You want to lease a car. dealership a has the car for $1500 down-payment and costs $200 per month. dealership b has a $3000 down-payment and is $75 per month. when do they cost the same? what is the cost?

In 12 months the amount paid to both dealerships will be equal.

The amount paid to each dealership = $3900

Step-by-step explanation:

Here,let x is the number of months when both the dealerships cost same.

DEALERSHIP - A

Fixed down payment =   $1500

The installment for each day  =  $200

⇒ Installments of x days  = x ( Installment for 1 day)  = $200 (x)  = 200 x

⇒ Total payment to Dealership

= Fixed amount + Installment amount in x days

= $1500 + 200 x

DEALERSHIP - B

Fixed down payment =   $3000

The installment for each day  =  $75

⇒ Installments of x days  = x ( Installment for 1 day)  = $75 (x)  = 75 x

⇒ Total payment to Dealership

= Fixed amount + Installment amount in x days

= $3000 + 75 x

Now, according to the question in x days, they both are paid same amount.

⇒$1500 + 200 x   = $3000 + 75 x

or, 200 x  - 75  x = 30000  - 1500

or, 125 x  =  1500

⇒ x = 1500 /125  = 12

or x  = 12

Amount paid  = $ 3000 + 75 x

                        = 3000 + 75(12)  = $3900

Hence, after 12 months the amount paid to both dealerships will be equal.

The amount paid to each dealership = $3900