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If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b?

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Bunuel
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If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b? [#permalink] New post   04 Apr 2017, 00:31
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If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b?

A. 11/12
B. 13/12
C. 7/6
D. 17/12
E. 9/6
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Re: If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b? [#permalink] New post   04 Apr 2017, 01:06
8A=6B
=> a=3/4B
now, 4a+9b=4
=> 4(3/4b)+9b=4
=> 12b=4
=>b=1/3
=>a=1/4

a+2b=1/4+2/3=11/12---(A)
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Re: If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b? [#permalink] New post   04 Apr 2017, 12:49
4a + 9b = 4
8a = 6b
4a = 3b

3b + 9b = 4
12b = 4
b = 1/3

4a + 9(1/3) = 4
4a + 3 = 4
4a = 1
a = 1/4

1/4 + 2(1/3)
1/4 + 2/3
11/12

Answer is A
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Re: If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b? [#permalink] New post   05 Apr 2017, 05:17
Bunuel wrote:
If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b?

A. 11/12
B. 13/12
C. 7/6
D. 17/12
E. 9/6



4a + 9b = 4......Multiply * 2

8a+ 18b=8.......Substitute from 8a = 6b

6b+18b=8......24b=8......b=1/3 & a=1/4

No need to calculate at all Because 1/3+ 1/4 <1. All answer choices are GREATER THAN 1 except one choice.

Answer: A
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Re: If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b? [#permalink] New post   14 Apr 2017, 05:48
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Bunuel wrote:
If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b?

A. 11/12
B. 13/12
C. 7/6
D. 17/12
E. 9/6


We can divide the equation 8a = 6b by 2 and we have 4a = 3b or 4a - 3b = 0.

We can then subtract 4a - 3b = 0 from 4a + 9b = 4 and we have:

12b = 4

b = 4/12 = 1/3

Thus:

4a = 3(1/3)

4a = 1

a = 1/4

So a + 2b = 1/4 + 2/3 = 3/12 + 8/12 = 11/12.

Answer: A
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Re: If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b? [#permalink] New post   14 Apr 2017, 07:24
Bunuel wrote:
If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b?

A. 11/12
B. 13/12
C. 7/6
D. 17/12
E. 9/6


\(8a + 18b = 8\)

Or, \(6b + 18b = 8\)

Or, \(24b = 8\)

So, \(b = \frac{1}{3}\)

Given , \(8a = 6b\)

So, \(8a = 6*\frac{1}{3}\)

Or, \(8a = 2\)

Or, \(a = \frac{1}{4}\)

Value of \(a + 2b = \frac{1}{4} + \frac{2}{3} = \frac{11}{12}\)

Hence, answer must be (A) \(\frac{11}{12}\)
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Re: If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b? [#permalink] New post   16 Jul 2017, 18:29
multiply first one by 2:
8a+18b=8
rewrite second one as:
8a-6b=0

subtract from first one the second one, and we get
24b=8
b=1/3
4a+ 9/3 = 4
4a=1
a=1/4

1/3 + 1/4 = 11/12
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If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b? [#permalink] New post   17 Jul 2017, 11:11
Bunuel wrote:
If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b?

A. 11/12
B. 13/12
C. 7/6
D. 17/12
E. 9/6



ANSWER:
=====

8a=6b
a= 6b/8 = 3b/4

4a + 9b = 4

substitute a= 3b/4
4(3b/4) + 9b = 4
b= 4/12 = 1/3

a = 3b/4
Substitue b= 1/3
a= 1/4

Value of a+2b=1/4+2/3=11/12

A
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Re: If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b? [#permalink] New post   29 Jun 2020, 04:17
IMo A

4a + 9b = 4
8a = 6b
4a = 3b

3b + 9b = 4
12b = 4
b = 1/3

4a + 9(1/3) = 4
4a + 3 = 4
4a = 1
a = 1/4

1/4 + 2(1/3)
1/4 + 2/3
11/12
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Re: If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b? [#permalink] New post   01 Jul 2020, 12:15
4a + 9b = 4
8a = 6b

3b + 9b = 4
12b = 4
b = 1/3

a = (6*1)/(3*8)
= 1/4

a+2b = 1/4 + 2*1/3
= 11/12
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Re: If 4a + 9b = 4 and 8a = 6b, what is the value of a + 2b? [#permalink]
01 Jul 2020, 12:15
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