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Sub 505 Level|   Algebra|      
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Bunuel
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If b = (c + d^2)/c and a = c/d^2, what is b in terms of a ? 18 Jun 2018, 21:32
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5% (low)

Question Stats:

92% (01:05) correct 8% (02:20) wrong based on 108 sessions

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If \(b=\frac{c+d^2}{c}\) and \(a=\frac{c}{d^2}\), what is b in terms of a ?


A. \(1+\frac{1}{a}\)

B. \(1+a\)

C. \(\frac{1}{1+a}\)

D. \(a^2+1\)

E. \(\frac{a}{a+1}\)
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A
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If b = (c + d^2)/c and a = c/d^2, what is b in terms of a ? 18 Jun 2018, 21:44
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Bunuel
If \(b=\frac{c+d^2}{c}\) and \(a=\frac{c}{d^2}\), what is b in terms of a ?


A. \(1+\frac{1}{a}\)

B. \(1+a\)

C. \(\frac{1}{1+a}\)

D. \(a^2+1\)

E. \(\frac{a}{a+1}\)

\(b=\frac{c+d^2}{c}\) ==>\(1+\frac{d^2}{c}\)

Sub \(a=\frac{c}{d^2}\)

Hence A
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If b = (c + d^2)/c and a = c/d^2, what is b in terms of a ? 18 Jun 2018, 22:23
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Solution



Given:
    • \(b = \frac{c + d^2}{c}\)
    • \(a = \frac{c}{d^2}\)

To find:
    • The value of b, in terms of a

Approach and Working:
From the given expression of b, we can write
    • \(b = \frac{c + d^2}{c} = 1 + \frac{d^2}{c} = 1 + \frac{1}{a}\)

Hence, the correct answer is option A.

Answer: A
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If b = (c + d^2)/c and a = c/d^2, what is b in terms of a ? 18 Jun 2018, 23:16
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Bunuel
If \(b=\frac{c+d^2}{c}\) and \(a=\frac{c}{d^2}\), what is b in terms of a ?


A. \(1+\frac{1}{a}\)

B. \(1+a\)

C. \(\frac{1}{1+a}\)

D. \(a^2+1\)

E. \(\frac{a}{a+1}\)

Given,

b = [m]\frac{(c+[m]d^2[}{m])/c}[/m]
a =
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If b = (c + d^2)/c and a = c/d^2, what is b in terms of a ? 19 Jun 2018, 11:07
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Bunuel
If \(b=\frac{c+d^2}{c}\) and \(a=\frac{c}{d^2}\), what is b in terms of a ?


A. \(1+\frac{1}{a}\)

B. \(1+a\)

C. \(\frac{1}{1+a}\)

D. \(a^2+1\)

E. \(\frac{a}{a+1}\)
In steps. Given:
\(a=\frac{c}{d^2}\)
\(b=\frac{c+d^2}{c}\)

\(a\) and second term of \(b\) are reciprocals

Rewrite equation for \(b\). Split the numerator
\(b=(\frac{c}{c}+\frac{d^2}{c})=(1 +\frac{d^2}{c})\)

Second term is reciprocal of \(a\). Rewrite \(a\)
\(a=\frac{c}{d^2}\)
\(\frac{1}{a}=\frac{d^2}{c}\)

Isolate \(\frac{d^2}{c}\) in equation for \(b\)
\(b=1 +\frac{d^2}{c}\)
\(b-1=\frac{d^2}{c}\)

Now both \(a\) and \(b\) are in terms of \((\frac{d^2}{c})\). Set equations equal
\(b-1=\frac{1}{a}\)
\(b=\frac{1}{a}+1\)

Answer A
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If b = (c + d^2)/c and a = c/d^2, what is b in terms of a ? Updated on: 20 Jun 2018, 11:34
Originally posted by baru on 20 Jun 2018, 09:57.
Last edited by baru on 20 Jun 2018, 11:34, edited 1 time in total.
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b=c+d^2/c and a=c/d^2


lets assume c =1 and d =2


then b = (1+4)/1 = 5

a = 1/4

Test answers with these values , A fits ===> 1/a = 4 +1 = 5 = b---Option A
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If b = (c + d^2)/c and a = c/d^2, what is b in terms of a ? 20 Jun 2018, 11:09
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Took more time than i though i would! +1 for A
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If b = (c + d^2)/c and a = c/d^2, what is b in terms of a ? 23 Jan 2020, 03:39
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b=c+d^2/c and a=c/d^2


we can assume c =1 and d =2


then b = (1+4)/1 = 5

a = 1/4

therefore A is correct
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