If 1.5x = 0.04y, then the value of \(\frac{y-x}{y+x}\) is
2023
If 1.5x = 0.04y, then the value of \(\frac{y-x}{y+x}\) is
Answer: B. \(\frac{73}{77}\) — ConceptA proportion fixes the relative scale of two quantities. If x:y = a:b, we may write x = ak and y = bk for a nonzero scale factor k. A ratio built from…
- A.
\(\frac{730}{77}\)
- B.
\(\frac{73}{77}\)
- C.
\(\frac{71}{77}\)
- D.
More than one of the above
- E.
None of the above
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Correct answer: B
Concept
A proportion fixes the relative scale of two quantities. If x:y = a:b, we may write x = ak and y = bk for a nonzero scale factor k.
A ratio built from homogeneous linear expressions, such as (y-x)/(y+x), is unchanged by that common scale factor.
Application
Clear the decimals in 1.5x = 0.04y by multiplying by 100: 150x = 4y.
Divide by 2 to obtain 75x = 2y, so x:y = 2:75.
Let x = 2k and y = 75k. Then (y-x)/(y+x) = (75k-2k)/(75k+2k) = 73k/77k = 73/77.
Cross-check
Substituting x = 2 and y = 75 into the original equation gives 1.5×2 = 3 and 0.04×75 = 3. The equation is satisfied, and the expression evaluates to 73/77.