SOLUTION: Which of the following is the smaller of two positive integers whose product is 108 and whose sum is twice their difference? a.12 b.8 c.6 d.4 e.3

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Which of the following is the smaller of two positive integers whose product is 108 and whose sum is twice their difference? a.12 b.8 c.6 d.4 e.3      Log On


   

Question 902968: Which of the following is the smaller of two positive integers whose product is 108 and whose sum is twice their difference?
a.12
b.8
c.6
d.4
e.3
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Equation 1: A+%2A+B+=+108
Equation 2: A+%2B+B+=+2%2A%28A-B%29
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Solve equation 1 for one of the variables
Equation 1: A+%2A+B+=+108
Divide both sides by B
A+=+108%2FB
Plug (108/B) into equation 2 for A
Equation 2: A+%2B+B+=+2%2A%28A-B%29
108%2FB+%2B+B+=+2%2A%28%28108%2FB%29+-+B%29
Multiply everything by B
108+%2B+B%5E2+=+2B%2A%28%28108%2FB%29+-+B%29
Multiply the 2B trough on the right hand side
108+%2B+B%5E2+=+216B%2FB+-+2B%5E2
The B's cross out
108+%2B+B%5E2+=+216cross%28B%29%2Fcross%28B%29+-+2B%5E2
108+%2B+B%5E2+=+216+-+2B%5E2
Add 2B^2 to both sides
108+%2B+3B%5E2+=+216
Subtract 108 from both sides
3B%5E2+=+108
Divide both sides by 3
B%5E2+=+36
Take the square root of both sides
sqrt%28B%5E2%29+=+sqrt%2836%29
highlight%28B+=+6%29
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Plug 6 into equation 1 for B
Equation 1: A+%2A+B+=+108
A+%2A+%286%29+=+108
Divide both sides by 6
highlight_green%28A+=+18%29
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Since our two integers are 6 & 18, then 6 is the smaller number.