SOLUTION: Four times a number is three times the difference between thirty five and the number. Find the number.

Question 118135: Four times a number is three times the difference between thirty five and the number. Find the number.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let x represent the unknown number.
.
What is 4 times that number? It is 4 times x or 4x for short.
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What is the difference between 35 and the number? It is 35 - x. And what is 3 times that
difference? It is 3(35 - x).
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The problem says that 4 times the number (4x) is equal to 3 times the difference between
35 and the number ... 3(35 - x)
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So set these two quantities equal:
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4x = 3(35 - x)
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On the right side do the distributed multiplication by multiplying 3 times each of the
terms inside the parentheses. When you do that multiplication the equation becomes:
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4x = 105 - 3x
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Get rid of the -3x on the right side by adding 3x to both sides. On the right side the
-3x and the 3x being added cancel each other out. On the left side the 4x plus 3x becomes
7x ... so the equation is then:
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7x = 105
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Solve for x by dividing both sides of this equation by 7 and you get:
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x = 15
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The number that you were asked to find is 15.
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Check ... 4 time that number is 4 times 15 and that is 60. The difference between 35 and
the number is 35 - 15 and that is 20. And 3 times that number is 60. This tells you that
4 times the number does equal 3 times the difference between 35 and the number. So the answer
is correct. The unknown number does equal 15.
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Hope this helps you to understand the problem and how to solve it.
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Have a Happy New Year ...
.
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