World Problem Math Algebra Fraction

Question

The denominator of a fraction in simplest form is greater than the numerator by $3$. If $7$ is added to the numerator, and $5$ added to the denominator, then the fraction itself is increased by $\dfrac 1 2$. Find the original fraction.

I got the equation $\dfrac x {x+3} = \dfrac {2x+14} {x+8}$.

When I solve this, I get a weird answer. My equation might be wrong. Can someone help me?

Why did you write "1 2"? Is it 12? – The Chaz 2.0 Jan 23 '16 at 20:57 — The Chaz 2.0, Jan 23 '16 at 20:57

fosho · Answer 1 · 2016-01-23T21:04:17.767

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Suppose the fraction (in simplest form) is $\frac{a}{b}$.

Then from the first statement $$b = a+3$$

From the second statement $$\frac{a+7}{b+5} = \frac{1}{2}+\frac{a}{b}$$

You know have a simple system of equations which you can solve.

edited Jan 23 '16 at 21:04

answered Jan 23 '16 at 20:58

fosho

6,334

the 12 is supposed to be 1/2 – dan Jan 23 '16 at 21:03

K.Power · Answer 2 · 2016-01-23T21:58:48.937

1

Let $x$ be the numerator. Then:

$\frac{x}{x+3}+\frac{1}{2}=\frac{x+7}{x+8}$

$\frac{1}{2}(x+8)(x+3)+x(x+8)=(x+3)(x+7)$

Then solve the quadratic equation.

edited Jan 23 '16 at 21:58

answered Jan 23 '16 at 20:59

K.Power

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This would be my interpretation, assuming the string "1 2" in the OP is actually just $12$ – The Chaz 2.0 Jan 23 '16 at 21:00
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If it's not $12$ the OP is doing funkier maths than I ever did at that level. – K.Power Jan 23 '16 at 21:03
Another interpretation is viewing the 2 statements as independent. – fosho Jan 23 '16 at 21:05
its supposed to be 1/2 or 0.5 @Daniel – dan Jan 23 '16 at 21:18
I've edited my answer. Let me know if anything is unclear. – K.Power Jan 23 '16 at 21:19
@dan I got that, see my answer. – fosho Jan 23 '16 at 21:19
does x=2 @Daniel – dan Jan 23 '16 at 21:22
Try it yourself. Put $x=2$ into the equation and see if $LHS=RHS$ – K.Power Jan 23 '16 at 21:28
And no, $x \neq 2$ for this case. – fosho Jan 23 '16 at 21:29
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Shouldn't the 1/2 be added to the LHS not the RHS? This says the fraction decreased by 1/2 when you added 7 to the numerator and 5 to the denominator? Also, Daniel's answer doesn't give you two linear equations... – Sean English Jan 23 '16 at 21:53
Right on all counts. I've edited it. Apologies I should rather go on here after waking up not right before going to sleep. – K.Power Jan 23 '16 at 21:59

World Problem Math Algebra Fraction

2 Answers2