Question

Nancy is the proud owner of a new car. She paid $1,500 upfront and took out a loan for the rest of the amount. The interest rate on the loan is 5%. If the total cost of buying the car (including the interest Nancy owes) is more than $16,213.02, how much money did Nancy borrow?.1st Question: Assume that x represents the amount of money Nancy borrowed. Write an expression that represents the amount borrowed (the principal) plus the interest owed on that amount.

Answer 1

1st Question:

Assume that x represents the amount of money Nancy borrowed. The interest rate on the loan is 5%. This means that the amount of interest that on the loan would be

5/100 * x = 0.05x

An expression that represents the amount borrowed (the principal) plus the interest owed on that amount is

x + 0.05x

= 1.05x

Secondly

She paid $1,500 upfront and took out a loan of $x for the rest of the amount. If the total cost of buying the car (including the interest Nancy owes) is more than $16,213.02, it means that

1500 + 1.05x > 16,213.02

Subtracting 1500 from both sides of the equation, we have

1500 - 1500 + 1.05x > 16213.02 - 1500

1.05x > 14713.02

Dividing both sides of the inequality by 1.05, we have

1.05x/1.05 = 14713.02/1.05

x > 14012.4

The amount borrowed is greater than $14012.4