$P=67,000+2,820 m$ $\newline$ The total payments, $P$ , in dollars, made by a homeowner $m$ months after starting payments on a home mortgage is given by the equation. What is the best interpretation of $67$ , $000$ as shown in the given equation? $\newline$ Choose $1$ answer: $\newline$ (A) The first payment was $67$ , $000$ dollars. $\newline$ B The homeowner pays $67$ , $000$ dollars each month. $\newline$ C) The homeowner paid $67$ , $000$ dollars at the end of the first month. $\newline$ (D) The total of all payments made by the homeowner is $67$ , $000$ dollars.

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Grade 8

Evaluate a linear function: word problems

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P=67,000+2,820 m

\newline

The total payments,

P

, in dollars, made by a homeowner

m

months after starting payments on a home mortgage is given by the equation. What is the best interpretation of

67

000

as shown in the given equation?

\newline

Choose

1

answer:

\newline

(A) The first payment was

67

000

dollars.

\newline

B The homeowner pays

67

000

dollars each month.

\newline

C) The homeowner paid

67

000

dollars at the end of the first month.

\newline

(D) The total of all payments made by the homeowner is

67

000

dollars.

Equation Structure: The equation provided is $P = 67,000 + 2,820m$ . To interpret the meaning of $67,000$ in this context, we need to understand the structure of the equation. The variable $P$ represents the total payments made, and $m$ represents the number of months after starting payments. The number $67,000$ is a constant, which means it does not change with the number of months. This suggests that $67,000$ is a fixed amount that is part of the total payments from the beginning.
Elimination of Options: Looking at the options provided, we can eliminate option (B) because $67,000$ is not multiplied by $m$ , which would indicate a recurring monthly payment. Instead, it is a one-time payment that is added to the total payments from the start.
Correct Interpretation: Option (C) is also incorrect because the equation does not specify that the $67$,$000$ dollars are paid at the end of the first month; it is simply part of the initial total payment amount.
Correct Interpretation: Option (C) is also incorrect because the equation does not specify that the $67,000 dollars are paid at the end of the first month; it is simply part of the initial total payment amount.Option (D) is not correct because the equation implies that $$67$,$000$ dollars is part of the total payments made by the homeowner, but it is not the total of all payments. The total payments will increase each month by $2$ , $820$ dollars.
Correct Interpretation: Option (C) is also incorrect because the equation does not specify that the $67,000 dollars are paid at the end of the first month; it is simply part of the initial total payment amount.Option (D) is not correct because the equation implies that$ $67$ , $000$ dollars is part of the total payments made by the homeowner, but it is not the total of all payments. The total payments will increase each month by $2,820 dollars.Option (A) is the correct interpretation. The first payment or the initial amount paid by the homeowner when starting the mortgage is$ $67$ , $000$ dollars. This is because it is the constant term in the equation, representing the initial amount included in the total payments before any monthly payments are made.