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# If x/4 + 24/x = 5, what are the values of 3x - 7?

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Re: If x/4 + 24/x = 5, what are the values of 3x - 7? [#permalink]
x^2 - 20x + 96 = 0
(x-8)(x-12) = 0
x = 8 or 12

substituting these values in 3x - 7 gives us answer choice 5.
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Re: If x/4 + 24/x = 5, what are the values of 3x - 7? [#permalink]
rsanchez wrote:
If x/4 + 24/x = 5, what are the values of 3x-7?

1: 8
2: 8 and 24
3: 17
4: 12 and 29
5: 17 and 29

any takers?

x/4 + 24/x = 5 => x^2-20x+96 = 0

x could be either 12 or 8

thus 3x-7 could be either 29 or 17

E
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Re: If x/4 + 24/x = 5, what are the values of 3x - 7? [#permalink]
solving for x and substituing in 3x-7 would give the answer E.
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Re: If x/4 + 24/x = 5, what are the values of 3x - 7? [#permalink]
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$$\frac{x}{4} + \frac{24}{x} = 5$$

$$\frac{x^2+96}{4x} = 5$$

$$x^2 - 20x + 96 = 0$$

x = 12 OR x = 8

3x-7 = 17 OR 29

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Re: If x/4 + 24/x = 5, what are the values of 3x - 7? [#permalink]
given expression can bededuced to x^2 -20x+96 =0 => x values are 8 and 12

substituting 8 and 12 in the 3x-7 gives 17 and 29 respectively
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Re: If x/4 + 24/x = 5, what are the values of 3x - 7? [#permalink]
rsanchez wrote:
If x/4 + 24/x = 5, what are the values of 3x - 7?

A. 8
B. 8 and 24
C. 17
D. 12 and 29
E. 17 and 29

Hi,
Another way for those who have difficulty in factorising..
Check for values of 3x-7..
A) 3x-7=8....x=5 substitute in the equation..
You don't get 5 ..
B) same as A..
C) 17=3x-7.....x=8
Substitute in equation..
8/4 + 24/8 = 2+3=5.. correct.
SO 17 is correct and thus we can check for choices where 17 is a choice..
So we can skip D
D) 12=3x-7... substitute and you don't get 5
E) 17 is correct,lets check 29..
3x-7=29...x=12..
Substitute in equation 12/4 + 24/12 = 3+2=5.. correct

E
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Re: If x/4 + 24/x = 5, what are the values of 3x - 7? [#permalink]

Solution

Given:
• x/4 + 24/x = 5

To find:
• We need to find the value of 3x-7.

Approach and Working:
• x/4 + 24/x = 5
o x2+96/4x= 5
o x2+96-20x=0
o (x-12)(x-8)=0
o Thus, x=12 and 8

• For x= 12
o 3x-7= 29

• For x= 8
o 3x-7= 17

Hence, the correct answer is option E.

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Re: If x/4 + 24/x = 5, what are the values of 3x - 7? [#permalink]
rsanchez wrote:
If x/4 + 24/x = 5, what are the values of 3x - 7?

A. 8
B. 8 and 24
C. 17
D. 12 and 29
E. 17 and 29

Responding to a PM

Quote:
Hey!

I hope you're well.

I'm having a little trouble with re-applying above equation out of a fraction format, may you kindly step-by-step, show me how to do this please? I would greatly appreciate it.

$$\frac{x}{4} + \frac{24}{x} = 5$$...
Get the LCM of denominators of two fractions - 4 and x, so LCM is 4x...
so LHS = $$\frac{x}{4} + \frac{24}{x} = \frac{x*x+4*24}{4x}=\frac{x^2+96}{4x}=5$$ = RHS
now multiply both sides by 4x...
$$\frac{x^2+96}{4x}=5............\frac{x^2+96}{4x}*4x=5*4x.........x^2+96=20x...........x^2-20x+96=0............x^2-12x-8x+96=0...........x(x-12)-8(x-12)=0............(x-12)(x-8)=0$$, so x can be 12 or 8
1) x=12, 3x-7=3*12-7=36-7=29
2) x=8, 3x-7=3*8-7=24-7=17
so E
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Re: If x/4 + 24/x = 5, what are the values of 3x - 7? [#permalink]
rsanchez wrote:
If x/4 + 24/x = 5, what are the values of 3x - 7?

A. 8
B. 8 and 24
C. 17
D. 12 and 29
E. 17 and 29

We can eliminate options by back solving. The good thing is that multiple options have the same value so it makes the process faster. But mind you, all calculations I am showing below need to be done orally. Else, this method is not worth it and you might as well make a quadratic and solve.

The options give the values of 3x - 7.

If 3x - 7 = 8, x = 5
5/4 + 24/5 do not give an integer. Hence eliminate (A) and (B)

If 3x - 7 = 17, x = 8
8/4 + 24/8 = 5 (Fits)

If 3x - 7 = 29, x = 12
12/4 + 24/12 = 5 (Fits)

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Re: If x/4 + 24/x = 5, what are the values of 3x - 7? [#permalink]
rsanchez wrote:
If x/4 + 24/x = 5, what are the values of 3x - 7?

A. 8
B. 8 and 24
C. 17
D. 12 and 29
E. 17 and 29

x/4 + 24/x = 5
$$x^2 + 96 = 20x$$
$$x^2 - 20x + 96 = 0$$
$$x^2 - 12x - 8x + 96 = 0$$
$$(x - 12) (x - 8) = 0$$
x = 12,8

3x - 7 = 29, 17