9514 1404 393
Answer:
20 . . . . value of last equation
(A, B, C) = (4, 5, 10) or (3 1/3, 6, 12) . . . . values of symbols
Explanation:
If we call the symbols, in order of appearance, A, B, C, then the equations are ...
2AB = 40 ⇒ AB = 20
2C/B = 4 ⇒ C/B = 2
Multiplying the second equation by the first, we get ...
(C/B)(AB) = AC = (2)(20) = 40 ⇒ AC = 40
Then the last equation is ...
(C-B)A = __
AC -AB = __ = 40 -20 = 20
The value of the last equation is 20.
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Per the above, we have AC = 40. The third equation is ...
(C +3A) = 22
Using the first relation, we have A = 40/C, so the second becomes ...
C +3(40/C) = 22
C² -22C +120 = 0
(C -10)(C -12) = 0
C = 10 or 12
As you can see, there are two possible solutions for the values of the symbols. The corresponding values of the other variables are ...
A = 40/C = 4 or 3 1/3
B = 20/A = C/2 = 5 or 6
The values of the variables are ...
(A, B, C) = (4, 5, 10) or (3 1/3, 6, 12)