Answer:
The amount that Nancy borrowed is greater than $109250 .49524
Step-by-step explanation:
In order to buy the new car, Nancy
paid $1,500 up front and took out a loan for the rest of the amount.
Let x = The amount of loan that she took.
The interest rate on the loan is 5%.
This means that she paid interest of 5/100 × x = 0.05 × x
= 0.05x
If the total cost of buying the car (including the interest Nancy owes) is more than $16,213.02,
It means that
1,500 + x + 0.05x is greater than 16,213.02
1500 + 1.05x = 16213.02
1.05x = 16,213.02 - 1500
1.05x = 114713.02
x = 114713.02/1.05
x = $109250 .49524
The amount that Nancy borrowed is greater than $109250 .49524
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.
amount borrowed + interest= = x+5% of x
= x+5100x
= x+0.05x
= 1.05x
The expression 1.05x represents the sum of the amount Nancy borrowed and the interest she owes on that amount.
B= Write an expression to represent Nancy’s total cost of buying the car.
Total Cost= (amount borrowed + interest) + Initial Payment
= 1.05x+1,500
C= Write an inequality using the expression from part B to represent this scenario.
The problem statemet says the total cost is more than $16,213.02:
Total cost>16,213.02
The inequality 1.05x + 1,500> 16,213.02 represents the scenario.
D= Solve the inequality for the variable x. Use opposite operations on both sides of the inequality until you get x on one side of the inequality by itself.
1.05x + 1,500> 16,213.02
1.05x > 16,213.02 - 1,500 (subtract 1,500 from both sides)
1.05x > 14,713.02
X > 14,713.02/1.05 (divide both sides by 1.05)
X > 14,012.40
E=What does the result from part D tell you about Nancy’s situation?
The inequality X> 14,012.04 means Nancy borrowed more than 14,012.40
F= Think about graphing the inequality you found in part D on a number line. What would it look like?
Choose the correct number:
open circle on 14,012.40 and arrow pointing right
open circle on 14,012.40 and arrow pointing left
closed circle on 14,012.40 and arrow pointing right
closed circle on 14,012.40 and arrow pointing left
Number 1 is correct. The graph of the inequality x > 14,012.40 has an open circle on 14,012.40 and an arrow pointing to the right.
