SOLUTION: The numerator of a fraction is seven more than twice the denominator. The value of the reciprocal of the fraction is 0.4. Find the original fraction. Could someone please help m

Question 120847: The numerator of a fraction is seven more than twice the denominator. The value of the reciprocal of the fraction is 0.4. Find the original fraction.
Could someone please help me?
Found 3 solutions by checkley71, Earlsdon, solver91311:
Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
(2x+7)/x=.4
2x+7=.4x
2x-.4x=-7
1.6x=-7
x=-7/1.6
x=-4.375 answer.
proof
(2*-4.375+7)/-4.375=.4
(-8.75+7)/-4.375=.4
-1.75/-4.375=.4
.4=.4

Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Let N = the numerator and D = the denominator, so the fraction can be written as: .
From the problem, you can write:
so we'll substitute the N with 2D+7 to get:
and the reciprocal of this is 0.4, so...
Replace the 0.4 with its fractional equvalent of
Now cross-multiply.
Simplify and solve for D.
Subtract 8D from both sides.
Divide both sides by 2.
and...

The original fraction is:

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!
Let x be the denominator. Twice the denominator is then 2x and seven more than that is 2x + 7, so our fraction is .

Since the value of the reciprocal of the fraction is 0.4, we can represent the reciprocal as . Therefore the value of the fraction itself must be .

Now we have enough information to create an equation:

Multiply both sides by 4, and then multiply both sides by x:

Distribute:

Add -10x to both sides:

Add -28 to both sides:

Divide by -2:

Check the answer:

, answer checks.
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