SOLUTION: translate and solve when twice a number is subtracted from twenty-four, the result is six times the number. find the number

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Question 80399: translate and solve
when twice a number is subtracted from twenty-four, the result is six times the number. find the number
Found 2 solutions by tutor_paul, bucky:
Answer by tutor_paul(519) (Show Source):
You can put this solution on YOUR website!
Here is the translation of the word problem into an equation:

Now, solve for x.
First, combine the x terms alone on one side of the equation:

Divide each side of the equation by 8 and you are done:

Good Luck,
tutor_paul@yahoo.com

Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
You are looking for a number ... so let's call the missing number X.
.
When "twice a number (or 2X) is subtracted from 24" is a statement that translates to:
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24 - 2X
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The problem says that the result equals 6 times the number (or 6X)
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Set this up as an equation:
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24 - 2X = 6X
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Solve this equation by first getting all the terms containing X on one side of the equal sign
and all the plain numbers on the other side. You can do this by adding 2X to the left
side to cancel out the -2X. But if you add 2X to the left side, you must also add 2X to the
right side to keep the equation in balance. Adding 2X to both sides results in:
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24 - 2X + 2X = 6X + 2X
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combining the -2X and +2X on the left side results in them canceling out and this
makes the equation become just:
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24 = 6X + 2X
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Combining the 6X and +2X on the right side makes the equation:
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24 = 8X
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Solve by dividing both sides of this equation by 8 and you get:
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24/8 = X
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and after doing the division on the left side you get the answer of:
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X = 3
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as being the number you are trying to find.
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Check ... from 24 subtract twice the number ... this is 24 - (2*3) = 24 - 6 = 18. Does
that equal 6 times the number or 6 times 3? 6 times 3 also equals 18. So the answer checks.
.
Hope this helps you to see how you just start breaking down a problem and converting
the given information into algebraic terms. Then solve the equation that results from
relating the algebraic terms to each other.
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