Question

Numerele naturale ab si bc cu bara deasupra, sunt scrise in baza 10 si sunt direct proportionale cu numerele 5 si respectiv 3.Aflati cifrele a,b si c.
URGENT!!

Answer 1

ab/bc = 5/3

a, b, c sunt cifre

3 × ab = 5 × bc

3 × (10a + b) = 5 × (10b + c)

30×a + 3×b = 50×b + 5×c

30×a = 47×b + 5×c

30×a - 5×c = 47×b

5 × (6×a - c) = 47×b

47×b = M5

47×b = 47×5 => b = 5
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6 × a - c = 47

c = 6×a - 47; 6×a > 47 => a > 8 => a = 9
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c = 6 × 9 - 47

c = 54 - 47

c = 7
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a = 9
b = 5
c = 7
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ab/bc = 95/57 = 5/3 (adevarat)