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Two positive integers A and B satisfy the following conditions 25 Sep 2019, 10:41
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35% (medium)

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80% (02:20) correct 20% (02:42) wrong based on 56 sessions

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Two positive integers A and B satisfy the following conditions: 9\(A^2\) = 12A + 96 and \(B^2\) = 2B + 3. What is the value of 5A + 7B ?

(A) 31

(B) 36

(C) 41

(D) 43

(E) 47

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C
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Two positive integers A and B satisfy the following conditions 25 Sep 2019, 10:51
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B²-2B-3=0
(B-3)(B+1)=0
B=3 ✔,-1✖
7B=21
A=4
Option C

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Two positive integers A and B satisfy the following conditions 30 Sep 2019, 18:28
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Can anyone please give an answer with more workings?
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Two positive integers A and B satisfy the following conditions 03 Oct 2019, 05:07
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9А^2=12A+96
Then, we decompose 96 into 4 and -100 to make a quadratic equation
(9A^2)-12A+4-100=0
((3A-2)^2)-10^2=0
As we know, that: a^2-b^2=(a-b)(a+b),
(3A-2-10)(3A-2+10)=0
(3A-12)(3A+8)=0
A=4; A=-(8/3)
As A is a positive integer, we choose A=4

The same thing we do with the second equation f(B)
We get B=3

Then we just put our resulted A and B into our main equation:
5A+7B=(5*4)+(7*3)=20+21=41
Option C

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