If 5a : 2b = 3 : 2 and 3b : 7c = 5 : 7, what is a : b : c?
2019
If 5a : 2b = 3 : 2 and 3b : 7c = 5 : 7, what is a : b : c?
Answer: C. 3 : 5 : 3 — ConceptA ratio equation can be read as a fraction. Cross-multiplication converts it into a ratio between the variables. When two ratios share a variable,…
- A.
5 : 3 : 7
- B.
7 : 5 : 3
- C.
3 : 5 : 3
- D.
5 : 7 : 3
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Correct answer: C
Concept
A ratio equation can be read as a fraction. Cross-multiplication converts it into a ratio between the variables.
When two ratios share a variable, scale them so that the shared term has the same value, and then combine the three terms.
Application
From 5a : 2b = 3 : 2, write 5a/(2b) = 3/2. Cross-multiplication gives 10a = 6b, so a : b = 3 : 5.
From 3b : 7c = 5 : 7, write 3b/(7c) = 5/7. Cross-multiplication gives 21b = 35c, so b : c = 5 : 3.
The common term b already has value 5 in both ratios. Therefore, a : b : c = 3 : 5 : 3.
Cross-check
Take a = 3, b = 5, and c = 3. Then 5a : 2b = 15 : 10 = 3 : 2, and 3b : 7c = 15 : 21 = 5 : 7. Both given ratios are satisfied.
Result
Thus, a : b : c = 3 : 5 : 3.