Cole buys a new laptop for $335. ?He makes a down payment of $50 ?and pays the rest in six equal monthly payments, P. ?What equation represents the relationship between the cost of the laptop and coles payments?
The Correct Answer and Explanation is :
The equation that represents the relationship between the cost of the laptop and Cole’s payments is:
[
335 = 50 + 6P
]
Explanation:
Let’s break this down step-by-step.
- Total Cost of the Laptop: The total cost of the laptop is $335. This is the amount Cole is paying for the laptop in total.
- Down Payment: Cole makes a down payment of $50. This means that, upfront, he has already paid $50, and he will still need to pay the remainder of the cost through monthly payments.
- Remaining Balance: After the down payment of $50, the remaining balance that Cole needs to pay is:
[
335 – 50 = 285
]
So, Cole still needs to pay $285 after the down payment.
- Monthly Payments: Cole will pay off the remaining balance in six equal monthly payments. Let’s represent each of these payments as ( P ). The total of these six payments will cover the remaining balance of $285.
- Total of Payments: The total of the six monthly payments is represented by:
[
6P
]
- Equation Setup: The total cost of the laptop, which is $335, is the sum of the down payment ($50) and the total of the six monthly payments (6P). Therefore, the equation becomes:
[
335 = 50 + 6P
]
Solving for ( P ):
To find out the amount of each monthly payment, we can solve for ( P ).
- Subtract 50 from both sides:
[
335 – 50 = 6P
]
[
285 = 6P
]
- Now, divide both sides by 6:
[
P = \frac{285}{6} = 47.5
]
Thus, each monthly payment ( P ) is $47.50.
This equation helps us understand how the total cost of the laptop is split between the down payment and the six equal monthly payments.