Question

Can Someone please please Please help on this. it is due tonight by midnight :( Thank you so much if you can..

QUESTIONS

Answer each of the following questions. Note that you may use a calculator (where necessary). However, you should show all steps to illustrate the process that you used to get your results.

Suppose that you are given the following scenario:
1. Betty is purchasing a car. She makes a $500 down payment on the car. Then, she needs to make a $275 monthly payment for 24 months. If she makes all of the monthly payments on time, she will get a $300 refund.

(A) Write a numerical expression (that correctly utilizes order of operations) to represent the total cost of the car if Betty makes all of the monthly payments on time.

(B) Simplify the numerical expression to find the total cost of the car if Betty makes all of the monthly payments on time.


2. For each of the following situations, the final answers shown are INCORRECT. Identify and explain the error that was made in the application of order of operations. Then, show the correct process and result.


3. Heidi is putting a garden in her backyard. She wants the garden to be rectangular. She also wants to use 120 feet of fencing to surround the garden. If the length of the garden needs to be 10 feet longer than the width, what should the dimensions (i.e., the length and the width) of the garden be? Use to represent the width of the garden. Set up an equation that could be used to solve for the width, and then solve the equation.

Answer 1

Step-by-step explanation:

1. (A) To represent the total cost of the car if Betty makes all of the monthly payments on time, we can use the following numerical expression, which correctly utilizes order of operations:

Total cost = (24 x $275) - $500 + $300

Step-by-step explanation:

24 x $275 represents the total amount of money Betty will pay in monthly installments over 24 months.

$500 represents the initial down payment.

$300 represents the refund that Betty will receive if she makes all of the monthly payments on time.

(B) To simplify the numerical expression and find the total cost of the car, we can perform the multiplication and addition/subtraction in the correct order:

Total cost = (24 x $275) - $500 + $300

Total cost = $6,600 - $500 + $300

Total cost = $6,400

Therefore, if Betty makes all of the monthly payments on time, the total cost of the car will be $6,400

3. Let's represent the width of the garden by x.

According to the problem, the length of the garden is 10 feet longer than the width, which means the length is x + 10.

We know that the perimeter of a rectangle is the sum of all its sides, so we can set up an equation:

2(x + x + 10) = 120

Simplifying this equation, we get:

4x + 20 = 120

4x = 100

x = 25

Therefore, the width of the garden is 25 feet and the length is x + 10 = 35 feet.

Now, let's identify the error in the application of the order of operations.

In the equation 2(x + x + 10) = 120, we need to simplify the expression inside the parentheses first.

2(x + x + 10) = 2(2x + 10) = 4x + 20

However, in the incorrect equation shown above, the expression inside the parentheses was simplified as 2x + 20 before multiplying by 2. This led to an incorrect value for x.

The correct process for solving the equation is:

2(x + x + 10) = 120

2(2x + 10) = 120

4x + 20 = 120

4x = 100

x = 25

Therefore, the dimensions of the garden should be 25 feet by 35 feet.