Question

building inequalities to solve real-world problems: tutorial
the expression 1.05x represents the sum of the amount nancy borrowed and the interest she owes on that amount.
part b
write an expression to represent nancys total cost of buying the car.
space used(includes formatting): 0 / 30000

Explanation:

Step1: Understand the context

We know that \(1.05x\) is the amount Nancy borrowed plus the interest. But to find the total cost of buying the car, we need to consider if there are other costs. However, since the problem is about writing the expression for total cost and we assume that the borrowed amount with interest is part of it, but maybe there's a down payment? Wait, no, the problem says "total cost of buying the car". Wait, maybe the \(1.05x\) is the loan with interest, but maybe there's a down payment? Wait, the problem doesn't mention a down payment, but maybe the original amount borrowed is \(x\), and \(1.05x\) is the loan plus interest. But maybe the total cost is the loan plus interest plus any other costs? Wait, the problem is probably assuming that the total cost is the amount she has to pay, which is the loan with interest. Wait, no, maybe the car's price is \(x\), and she borrowed \(x\) with 5% interest, so the total cost is \(1.05x\). Wait, but maybe there's a down payment? Wait, the problem statement is a bit unclear, but based on the given information, the expression \(1.05x\) is the sum of the borrowed amount and interest. So if that's part of the total cost, but maybe the total cost is that plus something? Wait, no, maybe the problem is that the car's price is \(x\), and she has to pay the loan (which is \(x\) with 5% interest) and maybe a down payment? Wait, the problem doesn't mention a down payment. Wait, maybe the total cost is just the amount she has to pay, which is \(1.05x\) plus maybe the down payment? But since the problem doesn't mention a down payment, maybe the total cost is \(1.05x\) plus the down payment, but we don't know the down payment. Wait, no, maybe the problem is that the car's price is \(x\), and she borrowed \(x\) with 5% interest, so the total cost is \(1.05x\). Wait, but maybe the original problem (before this part) had a down payment. Wait, since this is part B, maybe part A had a down payment. But since we only have part B, we assume that the total cost is the loan with interest. Wait, no, maybe the total cost is the down payment plus the loan with interest. But since we don't have the down payment amount, maybe the down payment is a constant? Wait, the problem is probably simpler. Wait, maybe the total cost is the amount she borrowed (with interest) plus the down payment. But since we don't have the down payment, maybe the down payment is, say, \(d\), but the problem doesn't mention it. Wait, this is confusing. Wait, maybe the problem is that the car's price is \(x\), and she pays a down payment of, say, \(y\), and then borrows \(x - y\) with 5% interest. But since the problem doesn't mention a down payment, maybe the total cost is \(1.05x\). Wait, maybe the problem is that the total cost is the loan amount (with interest) plus the down payment. But since we don't have the down payment, maybe the problem is assuming that the total cost is \(1.05x\) plus the down payment, but since we don't have the down payment, maybe the down payment is zero? No, that doesn't make sense. Wait, maybe the problem is that the total cost is the amount she has to pay, which is the loan ( \(x\) with 5% interest) and maybe the down payment. But since the problem is part B, maybe part A had a down payment. For example, if part A was about the down payment, say \(d\), then the total cost would be \(d + 1.05x\). But since we don't have that information, maybe the problem is that the total cost is \(1.05x\) plus the down payment, but since we don't know the down payment, maybe the problem is expecting us to write \(1.05x\) as the total cost, assuming that the down payment is zero or included in \(x\). Wait, this is a bit confusing, but based on the given information, the expression \(1.05x\) is the sum of the borrowed amount and interest. So if that's the amount she has to pay for the loan, and the total cost of the car is that plus any down payment. But since the problem doesn't mention a down payment, maybe the total cost is \(1.05x\). Wait, maybe the problem is that the car's price is \(x\), and she borrowed \(x\) with 5% interest, so the total cost is \(1.05x\). So the expression is \(1.05x\) plus any other costs, but since there are no other costs mentioned, the total cost is \(1.05x\).

Step2: Write the expression

Assuming that the total cost is the amount she has to pay, which is the loan with interest ( \(1.05x\) ) and there are no other costs, the expression for the total cost is \(1.05x\). Wait, but maybe the problem is that the car's price is \(x\), and she has to pay a down payment of, say, \(d\), and then borrow \(x - d\) with 5% interest. But since the problem doesn't mention a down payment, we can't include that. So based on the given information, the total cost is \(1.05x\).

Answer:

The expression to represent Nancy's total cost of buying the car is \(1.05x\) (assuming there are no additional costs mentioned; if there were a down payment or other costs, they would need to be included, but based on the given information, this is the expression).