Question

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?

Answer 1

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

The amount paid to each dealership = $3900

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