If f(t) = a + 9t and the sum of f(3), f(7), and f(11) is 279, what is a?
Answer and explanation
Correct answer: 30
The governing concept is substitution into a linear function followed by solving a one-variable equation. Evaluate each required function value: f(3) = a + 9(3) = a + 27, f(7) = a + 63, and f(11) = a + 99. Adding them gives (a + 27) + (a + 63) + (a + 99) = 3a + 189. The problem states that this sum is 279, so 3a + 189 = 279. Subtracting 189 gives 3a = 90, and dividing by 3 yields a = 30. Hence option A is correct. The coefficient of a is 3 because a appears in all three function values; overlooking that repetition or adding the numerical terms incorrectly can produce the distractors.
Frequently asked questions
What is the correct answer to this question?
30
Why is this the correct answer?
The governing concept is substitution into a linear function followed by solving a one-variable equation. Evaluate each required function value: f(3) = a + 9(3) = a + 27, f(7) = a + 63, and f(11) = a + 99. Adding them gives (a + 27) + (a + 63) + (a + 99) = 3a + 189. The problem states that this sum is 279, so 3a + 189 = 279. Subtracting 189 gives 3a = 90, and dividing by 3 yields a = 30. Hence option A is correct. The coefficient of a is 3 because a appears in all three function values; overlooking that repetition or adding the numerical terms incorrectly can produce the distractors.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear growth and decay.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
