If (3x + 5y) : (2x + 3y) = 29 : 18, then \(\frac{y}{x}\) is equal to
2025
If (3x + 5y) : (2x + 3y) = 29 : 18, then \(\frac{y}{x}\) is equal to
Answer: C. \(\frac{4}{3}\) — ConceptIf two linear expressions are in a given ratio, replace the ratio by an equation using cross-multiplication. After collecting the x-terms and y-terms,…
- A.
\(\frac{2}{3}\)
- B.
\(\frac{5}{6}\)
- C.
\(\frac{4}{3}\)
- D.
\(\frac{3}{4}\)
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Correct answer: C
Concept
If two linear expressions are in a given ratio, replace the ratio by an equation using cross-multiplication. After collecting the x-terms and y-terms, divide by x (with x nonzero) to obtain y/x.
Application
Write the proportion as (3x + 5y)/(2x + 3y) = 29/18.
Cross-multiply: 18(3x + 5y) = 29(2x + 3y).
Expand both sides: 54x + 90y = 58x + 87y.
Collect like terms: 90y - 87y = 58x - 54x, so 3y = 4x.
Divide by 3x: y/x = 4/3.
Cross-check
Put y = 4x/3. Then 3x + 5y = 29x/3 and 2x + 3y = 6x, whose ratio is (29x/3)/(6x) = 29/18. Therefore, y/x = 4/3.
Result
Therefore, y/x = 4/3.