Asked by Pajad

Find the value of A if (27\8)A+7=(4\9)-3A
Answered by Arora
(27\8)A+7=(4\9)-3A
=> (27/8)A + 3A = (4/9) - 7
=> A((27+24)/8) = (4-63)/7
=> (51/8)A = -59/7
=> A = -(59/7)*(8/51)
Answered by Bosnian
If (27\8)A+7=(4\9)-3A mean:

( 27 / 8 ) A + 7 = 4 / 9 - 3 A

then:

Add 3 A to both sides

27 A / 8 + 7 + 3 A = 4 / 9 - 3 A + 3 A

27 A / 8 + 7 + 24 A / 8 = 4 / 9

51 A / 8 + 7 = 4 / 9

Subtract 7 to both sides

51 A / 8 + 7 - 7 = 4 / 9 - 7

51 A / 8 = 4 / 9 - 63 / 9

51 A / 8 = - 59 / 9

Multiply both sides by 8

51 A = - 59 ∙ 8 / 9

51 A = - 472 / 9

Multiply both sides by 9

51 ∙ 9 A = - 472

459 A = - 472

Divide both sides by 459

A = - 472 / 459


But if 27 \ 8 mean the integer part of such a ratio ( integer division ) then:

( 27 \ 8 ) A + 7 = ( 4 \ 9 ) - 3 A

3 A + 7 = 0 - 3 A

3 A + 7 = - 3 A

Add 3 A to both sides

3 A + 7 + 3 A = - 3 A + 3 A

6 A + 7 = 0

Subtract 7 to both sides

6 A + 7 - 7 = 0 - 7

6 A = - 7

Divide both sides by 6

A = - 7 / 6


Answered by Reiny
If possible, I prefer to work without fractions

(27\8)A+7=(4\9)-3A
times 72
243A + 504 = 32 - 216A
459A = -472
A = -472/459

I verified this answer in the left and right sides.
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