SOLUTION: When a certain number is divided by 7, the result is the same as when this number is decreased by 12. What is the number? F)14 G)13 H)10 J) none of these

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Question 1144969: When a certain number is divided by 7, the result is the same as when this number is decreased by 12. What is the number?
F)14
G)13
H)10
J) none of these
Answer by ajspeller(2) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the unknown number
Let x%2F7 be the unknown number divided by 7
Let +x+-+12+ be the unknown number decreased by 12
Set the expressions equal to each other
x%2F7+=+%28x-12%29
Convert the right side to a fraction by placing it over 1
x%2F7+=+%28x-12%29%2F1
Cross multiply to get
+7%28x-12%29+=+x+%2A+1+
Simplify by distributing the 7
+x%287%29+-+12%287%29+=+x+%2A+1+
Simplify by multiplying
+7x+-+84+=+x
Combine like terms by subtracting 7x from both sides
+7x+-+7x+-+84+=+x+-+7x
Simplify
+0+=+84+=+-6x
Simplify
+-84+=+-6x+
Isolate x by dividing by sides by -6
+%28-84%29%2F%28-6%29+=+%28-6x%29%2F%28-6%29
Simplify, remember that a negative by a negative is a positive
+14+=+x+
Check:
x%2F7+=+%28x-12%29
Substitute in the +14+
+14%2F7+=+%2814-12%29
Evaluate
+2+=+2
Correct!