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Question 1039513: Eleven less than two third of twice the number and 19 is 95.find the number.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the number.
2/3 * the number and 19 is equal to 2/3 * (x + 19).
11 less than that is equal to 2/3 * (x + 19) - 11.
you get 2/3 * (x + 19) - 11 = 95.
add 11 to both sides of the equation to get 2/3 * (x + 19) = 106.
multiply both sides of the equation by 3/2 to get x + 19 = 3/2 * 106.
simplify this to get x + 19 = 159.
subtract 19 from both sides of the equation to get x = 140.
that should be your number.
your original equation is 2/3 * (x + 19) - 11 = 95.
if the number is 140, then 2/3 * (140 + 19) - 11 = 95.
do the math and you get 95 = 95 which confirms the solution is correct as long as the original equation is correct.
interpretation of the original problem statement is the key.
the original problem statement says:
Eleven less than two third of twice the number and 19 is 95. find the number.
this can be interpreted as:
2/3 * 2x + 19 - 11, ...
or it can be interpreted as:
2/3 * 2 * (x + 19) - 11.
the first interpretation didn't make a lot of sense because why would you add 19 and then subtract 11 and it also led to an answer that was not an integer,
the second interpretation made more sense and did lead to an integer answer.
the answer is that the number had to be 140 because 2/3 * (140 + 19) - 11 is equal to 95.
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