AnswersAlgebra 2 with ProbabilityIntroduction to Systems of Linear Equations — QuizQuestion 3
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QuizMultiple Choice

Introduction to Systems of Linear Equations — Quiz

Question 3 • Algebra 2 with Probability

Melinda takes out a loan to purchase a car. The balance on her loan after x months is represented by the equation y is equal to 10,000 minus 250 x and the value of the car after x months is represented by y is equal to 8,000 minus 50 x Which statement describes when Melinda’s loan will be equal to the value of the car?

Answer
A
After 14 months, the loan and value of the car will both be equal to 6,500 dollars .
B
After 12 months, the loan and value of the car will both be equal to 7,000 dollars .
C
After 10 months, the loan and value of the car will both be equal to 7,500 dollars .
D
After 16 months, the loan and value of the car will both be equal to 6,000 dollars .

Explanation

Set the loan balance equal to the car’s value: 10,000 − 250x = 8,000 − 50x. Solving gives 2,000 = 200x, so x = 10 months; substituting gives 10,000 − 250(10) = $7,500. Thus, after 10 months, both are $7,500, as choice C states.

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