Math  /  Algebra

QuestionXII. Харьцаа, пропгорц
46. a2b+c3c5b=13\frac{a-2 b+c}{3 c-5 b}=\frac{1}{3} бол ba=\frac{b}{a}= ?

Studdy Solution

STEP 1

1. The given equation is a proportion.
2. We need to solve for the ratio ba\frac{b}{a}.
3. We will use cross-multiplication to solve the proportion.

STEP 2

1. Cross-multiply to eliminate the fraction.
2. Simplify the resulting equation.
3. Solve for ba\frac{b}{a}.

STEP 3

Cross-multiply to eliminate the fraction in the equation:
a2b+c3c5b=13\frac{a-2b+c}{3c-5b} = \frac{1}{3}
Cross-multiplying gives:
3(a2b+c)=1(3c5b)3(a - 2b + c) = 1(3c - 5b)

STEP 4

Expand both sides of the equation:
3(a2b+c)=3a6b+3c3(a - 2b + c) = 3a - 6b + 3c
1(3c5b)=3c5b1(3c - 5b) = 3c - 5b
Set the expanded expressions equal to each other:
3a6b+3c=3c5b3a - 6b + 3c = 3c - 5b

STEP 5

Simplify the equation by subtracting 3c3c from both sides:
3a6b=5b3a - 6b = -5b
Add 6b6b to both sides to isolate terms involving aa:
3a=6b5b3a = 6b - 5b
Simplify the right side:
3a=b3a = b

STEP 6

Solve for ba\frac{b}{a} by dividing both sides by 3a3a:
b=3ab = 3a
ba=3aa=3\frac{b}{a} = \frac{3a}{a} = 3
The value of ba\frac{b}{a} is:
3\boxed{3}

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