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# Which number is a solution for x/4 + 5/ 4= x/8+ 3?

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Senior Manager
Joined: 02 Jan 2017
Posts: 307
Which number is a solution for x/4 + 5/ 4= x/8+ 3?  [#permalink]

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22 Feb 2017, 04:55
1
00:00

Difficulty:

5% (low)

Question Stats:

87% (01:15) correct 13% (01:33) wrong based on 62 sessions

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Which number is a solution for x/4 + 5/ 4= x/8+ 3?

A. −14
B. −7
C. 0
D. 7
E. 14
CEO
Joined: 11 Sep 2015
Posts: 3429
Re: Which number is a solution for x/4 + 5/ 4= x/8+ 3?  [#permalink]

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22 Feb 2017, 06:23
1
Top Contributor
1
vikasp99 wrote:
Which number is a solution for x/4 + 5/4 = x/8 + 3?

A. −14
B. −7
C. 0
D. 7
E. 14

Let's first eliminate the fractions by multiplying both sides of the equation by 8, which is the least common multiple of the denominators (4, 4, and 8)
We get: 8(x/4 + 5/4) = 8(x/8 + 3)
Expand to get: 2x + 10 = x + 24
Subtract x from both sides: x + 10 = 24
Subtract 10 from both sides: x = 14

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Eliminating fractions in equations:

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Re: Which number is a solution for x/4 + 5/ 4= x/8+ 3?  [#permalink]

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22 Feb 2017, 06:44
vikasp99 wrote:
Which number is a solution for $$\frac{x}{4} + \frac{5}{4}= \frac{x}{8}+ 3$$?

A. −14
B. −7
C. 0
D. 7
E. 14

$$\frac{x}{4} + \frac{5}{4}= \frac{x}{8}+ 3$$

Or, $$\frac{x + 5}{4} = \frac{x + 24}{8}$$

Or, $$2x + 10 = x + 24$$

Or, $$x = 14$$

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Re: Which number is a solution for x/4 + 5/ 4= x/8+ 3?  [#permalink]

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22 Feb 2017, 09:35
vikasp99 wrote:
Which number is a solution for x/4 + 5/ 4= x/8+ 3?

A. −14
B. −7
C. 0
D. 7
E. 14

Here you can solve quickly by algebraic method however other way is by substitute method

The only value for satisfying x/4 + 5/ 4= x/8+ 3 is 14

Hence E
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Re: Which number is a solution for x/4 + 5/ 4= x/8+ 3?  [#permalink]

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10 Feb 2019, 11:08
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Re: Which number is a solution for x/4 + 5/ 4= x/8+ 3?   [#permalink] 10 Feb 2019, 11:08
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