# Brandon is buying a car. The monthly payment, p, for the car varies directly with the amount...

## Question:

Brandon is buying a car. The monthly payment, p, for the car varies directly with the amount borrowed, b. Suppose that the dealership tells him that if he borrows $15,000, his payment will be$293.49. What would be his payment if he borrows \$18,000?

## Direct Variability

Two quantities are said to vary directly with each other when they both move in the same direction when the value of one changes. If the amount borrowed increases the loan payment increases and vice-versa. Therefore, the two quantities are directly proportional.

## Answer and Explanation:

As the monthly payment varies directly with the amount borrowed, we have:

$$p=kb$$

Here, k is the constant of proportionality. As p=293.49 when b=15000, we have:

\begin{align} &293.49=15000k\\ \therefore &k=0.019566 \end{align}

Now, the value of p when b=18000 will be:

\begin{align} p&=0.019566*18000\\ &=352.188 \end{align}