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Question

Don't really know what needs to be plugged into X and Y

 

Yearly Salary b4 taxes = $74,000

Monthly Salary = $6,166.66

Car cost $38,858

 

Bank A: y=1.25x+50

Bank B: y=1.3x

1) total cost of your vehicle using bank A

2) monthly payment of your vehicle using bank A
3) total cost of your vehicle using bank B
4) monthly payment of your vehicle using bank B

Answer 1

Let's work through this step by step! The good news is that once you understand what x and y represent, the calculations become much easier.

Step 1: Understand the variables.

We are given two equations:

Bank A: y = 1.25x + 50

Bank B: y = 1.3x

In these equations:

1. x = Original cost of the car
2. y = Total amount paid for the car, including the bank's additional charges

We know the car costs $38,858.

Therefore:

x = 38,858

The annual salary of $74,000 and monthly salary of $6,166.66 are not needed to calculate the total costs. However, they may be useful later when determining whether the monthly payments are affordable.

Question 1: What is the total cost of the vehicle using Bank A?

Bank A uses the equation:

y = 1.25x + 50

Substitute the car's price for x:

y = 1.25(38,858) + 50

First, multiply:

1.25 × 38,858 = 48,572.50

Now add $50:

y = 48,572.50 + 50

Bank A Total Cost = $48,622.50

This means you would pay $48,622.50 altogether under Bank A's pricing formula.

Question 2: What is the monthly payment using Bank A?

To calculate the monthly payment, divide the total cost by the number of months in the loan.

Monthly Payment = Total Cost / Number of Months

For Bank A:

Monthly Payment = 48,622.50 / Number of Months

The problem does not tell us how long the loan lasts, so we cannot determine one exact monthly payment.

However, let's look at an example.

If the loan lasts 5 years:

5 × 12 = 60 months

Monthly Payment = 48,622.50 / 60

Monthly Payment = $810.38

Therefore, with a 60-month loan, the monthly payment would be approximately $810.38.

Question 3: What is the total cost of the vehicle using Bank B?

Bank B uses the equation:

y = 1.3x

Substitute x = 38,858:

y = 1.3(38,858)

Multiply:

1.3 × 38,858 = 50,515.40

Bank B Total Cost = $50,515.40

This means you would pay $50,515.40 altogether under Bank B's pricing formula.

Question 4: What is the monthly payment using Bank B?

Again, we divide the total cost by the number of months.

Monthly Payment = 50,515.40 / Number of Months

If we assume a 5-year loan:

Monthly Payment = 50,515.40 / 60

Monthly Payment = $841.92

Therefore, with a 60-month loan, the monthly payment would be approximately $841.92.

Step 5: Compare the two banks.

Bank A:

1. Total cost = $48,622.50
2. Monthly payment for 60 months = $810.38

Bank B:

1. Total cost = $50,515.40
2. Monthly payment for 60 months = $841.92

Now calculate the difference in total cost:

$50,515.40 - $48,622.50 = $1,892.90

Bank A saves you $1,892.90 compared with Bank B.

Final Answers:

1. Total cost using Bank A = $48,622.50
2. Monthly payment using Bank A = $48,622.50 divided by the number of loan months
3. Total cost using Bank B = $50,515.40
4. Monthly payment using Bank B = $50,515.40 divided by the number of loan months

If the loan is for 60 months, the monthly payments would be $810.38 for Bank A and $841.92 for Bank B.

Which bank is better?

Based on the given equations, Bank A is the less expensive option because its total cost is $1,892.90 lower.

Important Reminder:

The exact monthly payments cannot be determined without knowing the loan term. The 60-month calculations are examples, not necessarily the answers your assignment expects.

The most important thing to remember is that x represents the original car price ($38,858), and y represents the total cost after applying each bank's formula. Once you substitute x into the equations, you can solve for y!