Please help with with the following math problem:?
Five ninths of a number is subtracted from six. The absolute value of the result is 3 times the original number. What is the largest number for which this is true?
Thanks a lot!
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Let the number be x.
Then:
|6 – (5x / 9)| = 3x
Option A:
6 – 5x / 9 >= 0
(54 – 5x) / 9 >= 0
54 – 5x >= 0
x <= 54 / 5 ......(1) and (54 - 5x) / 9 = 3x 54 - 5x= 27x 32x = 54 x = 27/16. This is compatible with (1). Option B: 6 - 5x / 9 < 0 54 - 5x < 0 x > 54/5 ……..(2)
and
5x / 9 – 6 = 3x
(5x – 54) / 9 = 3x
5x – 54 = 27x
x = -54 / 22
x = -27 / 11.
This is not compatible with (2).
The only solution meeting the requirement is that from option A, namely x = 27/16.
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