The value of which of the following can be determined if (a + 12b)/4b

Question

The value of which of the following can be determined if (a + 12b)/4b = 18/5?

I. a/b
II. 5b/(a + 7b)
III. (a + 3)/(b + 5)

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

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hinasingh · Answer

\frac{(a+12b)}{4b} =\frac{18}{5}
5a + 60b = 72b
=> 5a = 12b
=>\frac{ a}{b} = \frac{12}{5} 
Therefore, I can be determined.

Now,  \frac{(a+12b)}{4b} =\frac{18}{5} 
=>(a+7b +5b) =  \frac{18}{5} *4b
=> a + 7b =   \frac{72b}{5}  - 5b
=> a + 7b =  \frac{(72-25)b}{5 }= \frac{47b}{5} 
=> \frac{(a+7b)}{b }= \frac{47}{5} 
Taking reciprocal and multiplying both sides by 5, we get
=>  \frac{5b}{(a+7b)} = \frac{25}{47} 
therefore, II can be determined.

Since, we know that a/b = 12/5. we cannot find III.
Answer D

Beko · Answer

Hello,

"Since, we know that a/b = 12/5. we cannot find III." why is that?

Thank you in advance!

Best regards

hinasingh · Answer

Hi  Beko 
a/b = 12/5 => a = (12/5)*b. Add 3 to both sides
=> a + 3 = (12/5)b + 3.
From here, there is no way to make the coefficient of b 1.

Hope, this helps.

ThatDudeKnows · Answer

Beko

(a + 12b)/4b = 18/5
72b = 5a+60b
5a = 12b
a = 2.4b

I. a/2.4a = 1/2.4 
Need I, so eliminate B and C.

II. 5b/(2.4b+7b) = 5b/9.4b = 5/9.4
Need II, so eliminate A.

III. (2.4b+3)/(b+5)
If we use 0 for b, we get 3/5.
If we use 1 for b, we get 5.4/6, which is not the same as 3/5.
Cross out III, so eliminate E.

Answer choice D.

shivani1351 · Answer

Given:
(a + 12b)/4b = 18/5

Cross-multiplying, we get:
5a+60b = 72b
5a = 12b
Thus, a/b = 12/5

Hence, option 1 can be determined easily.

Now, let's check for option 2: 5b/(a + 7b)

a = 12b/5 => 5b/(12b/5 + 7b) = 25/47

Hence, option 2 can be determined as well.

Finally, let's check for option 3. We need to check if the value of (a + 3)/(b + 5) can be determined.

a = 12b/5

Trying for values of b using this:

Case 1: b = 5 => a = 12
Case 2: b = 10 => a = 24

Likewise, we can obtain more such combinations of a and b. Thus, we cannot uniquely determine the values of a and b.

Hence, we can only determine the values of Option 1 and 2. Thus, the correct option is Option (D) (Answer)

vasu1104 · Answer

(a + 12b) / 4b = 18/5
5a + 6b = 72b
5a = 12b
a / b = 12/5

value of option 1 and 2 can be easily found.
choice 3 doesnt give any particular value. so option D is correct ans

The value of which of the following can be determined if (a + 12b)/4b

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The value of which of the following can be determined if (a + 12b)/4b

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