SOLUTION: THE SUM OF A NUMBER AND 12 TIMES ITS RECIPROCAL IS 7. FIND THE NUMBER

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Question 115096: THE SUM OF A NUMBER AND 12 TIMES ITS RECIPROCAL IS 7. FIND THE NUMBER
Found 2 solutions by MathLover1, Fombitz:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

THE SUM OF A NUMBER AND 12 TIMES ITS RECIPROCAL IS 7. FIND THE NUMBER
let THE NUMBER be x,then
x+%2B+12+%281%2Fx%29+=+7..........multiply both sides by x
x%2Ax+%2B+12+%281%2Fx%29%2Ax+=+7%2Ax
x%5E2+%2B+12+=+7x.....move 7x to the left
x%5E2+-+7x+%2B+12+=+0.....use quadratic formula to solve for x
x%5B1%2C2%5D=%28-b+%2B-+sqrt+%28b%5E2+-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29
x%5B1%2C2%5D=%28-%28-7%29+%2B-+sqrt+%28%28-7%29%5E2+-4%2A1%2A12+%29%29+%2F+%282%2A1%29
x%5B1%2C2%5D=%287+%2B-+sqrt+%2849+-+48%29%29%2F2
x%5B1%2C2%5D=%287+%2B-+sqrt+%281%29%29%2F2
x%5B1%2C2%5D=%287+%2B-+1%29%2F2
x%5B1%5D=%287+%2B+1%29%2F2
x%5B1%5D=+8%2F2
x%5B1%5D=+4
x%5B2%5D=%287+-1%29%2F2
x%5B2%5D=+6%2F2
x%5B2%5D=+3
check:
x+%2B+12+%281%2Fx%29+=+7..........
4%2B+12+%281%2F4%29+=+7..........
4%2B+3+=+7..........
7+=+7


x+%2B+12+%281%2Fx%29+=+7..........
3+%2B+12+%281%2F3%29+=+7..........
3+%2B+4+=+7..........
7+=+7





Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call your number N.
N%2B12%2FN=7
N%5E2%2B12=7N Multiply both sides by N.
N%5E2-7N%2B12=0
%28N-4%29%28N-3%29=0
Two solutions
N=3 and N=4.
Check your answers.
1. 3+%2B+12%2F3+=+7
3+%2B+4+=+7
7=7
True statement.
2. 4+%2B+12%2F4+=+7
4%2B3=7
7=7
True statement.
Good answers.