Question

lesson activity
representing and solving problems with two-step inequalities
this activity will help you meet these educational goals:
mathematical practices—you will make sense of problems and solve them, reason abstractly and quantitatively, attend to precision, look for and make use of structure, and express regularity in repeated reasoning.
directions
read the instructions for this self - checked activity. type in your response to each question, and check your answers. at the end of the activity, write a brief evaluation of your work.
activity
nancy is the proud owner of a new car. she paid $1,500 up front 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?
complete the steps below to solve the problem.
part a
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.

Explanation:

Step1: Recall simple interest formula

The simple interest formula is \( I = Prt \), but since it's a one - time loan (we can assume \( t = 1 \) year for simplicity as the time period isn't specified otherwise), the interest \( I \) on principal \( P=x \) with rate \( r = 5\%=0.05 \) is \( I=0.05x \).

Step2: Find total amount (principal + interest)

The principal is \( x \) and the interest is \( 0.05x \). So the total amount (principal + interest) is the sum of the principal and the interest. That is \( x+0.05x \) or we can factor out \( x \) to get \( x(1 + 0.05)=1.05x \).

Answer:

The expression is \( 1.05x \) (or \( x + 0.05x \))