SOLUTION: michael has a sister who is three years older than he is, and a brother who is two years younger than he is. how old must michael be in order that the ratio of his sisters age to h

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Question 1147929: michael has a sister who is three years older than he is, and a brother who is two years younger than he is. how old must michael be in order that the ratio of his sisters age to his brothers age is less than 2?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = Michael's age
+x+%2B+3+ = his sister's age
+x+-+2+ = his brother's age
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+%28+x+%2B+3+%29+%2F+%28+x++-+2+%29+%3C+2+
+x+%2B+3+%3C+2%2A%28+x+-+2+%29+
+x+%2B+3+%3C+2x+-+4+
+3+%3C+x+-+4+
+7+%3C+x+
I can write this in the other direction:
+x+%3E+7+
Michael must be older than 7
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check:
suppose +x+=+7+
+%28+7+%2B+3+%29+%2F+%28+7+-+2+%29+%3C+2+
+10+%2F+5+=+2+
+10+%3C+10+ not true
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suppose +x+=+6+
+%28+6+%2B+3+%29+%2F+%28+6+-+2+%29+%3C+2+
+9+%2F+4+%3C+2+
+9+%3C+8+ not true
+x+%3E+7+ is the answer