If 4 ≤ x ≤ 8 and 2 ≤ y ≤ 7 , then what is the ratio of maximum value of (x + y) to minimum value of (x - y) ?
- A6
- B(15)/(2)
- C-(15)/(2)
- DNone of the aboveCorrect
Explanation
To find the ratio, we first need to determine the maximum value of (x + y) and the minimum value of (x - y).
Given ranges: 4 <= x <= 8 2 <= y <= 7
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Maximum value of (x + y): To maximize (x + y), we take the maximum possible values for both x and y. Max (x + y) = x_max + y_max = 8 + 7 = 15.
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Minimum value of (x - y): To minimize (x - y), we take the minimum possible value for x and the maximum possible value for y. This makes the subtracted part as large as possible, resulting in the smallest difference. Min (x - y) = x_min - y_max = 4 - 7 = -3.
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Ratio of maximum value of (x + y) to minimum value of (x - y): Ratio = (Max (x + y)) / (Min (x - y)) Ratio = 15 / (-3) Ratio = -5
Now, let's check the given options: A) 6 B) (15)/(2) = 7.5 C) -(15)/(2) = -7.5 D) None of the above
Our calculated ratio is -5, which is not present in options A, B, or C. Therefore, the correct answer is D.
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