Simultaneously 6563

The fraction will have a value of 3 if we increase the numerator (a) by 1 and simultaneously decrease the denominator (b) by 2. However, if we simultaneously decrease the numerator and the denominator by 1, the fraction will have a value of 1/2. What fraction is a/b?

Correct answer:

a =  2
b =  3

Step-by-step explanation:

a+1 = 3 (b-2)
(a-1) = 1/2 · (b-1)

a+1 = 3·(b-2)
(a-1) = 1/2 · (b-1)

a-3b = -7
2a-b = 1

Pivot: Row 1 ↔ Row 2
2a-b = 1
a-3b = -7

Row 2 - 1/2 · Row 1 → Row 2
2a-b = 1
-2.5b = -7.5


b = -7.5/-2.5 = 3
a = 1+b/2 = 1+3/2 = 2

a = 2
b = 3

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