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If a : b = 3 : 2, then (5a + 2b) : (3a + 4b) is equal to:
- a)16 : 15
- b)8 : 7
- c)19 : 17
- d)17 : 14
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If a : b = 3 : 2, then (5a + 2b) : (3a + 4b) is equal to:a)16 : 15b)8...
A : b = 3 : 2
Then, (5a + 2b) : (3a + 4b)
a/b = 3/2
So, a = 3 and b = 2
(5 × 3 + 2 × 2) : (3 × 3 + 4 × 2)
= 19 : 17
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Community Answer
If a : b = 3 : 2, then (5a + 2b) : (3a + 4b) is equal to:a)16 : 15b)8...
Given Ratio:
- Let a = 3x and b = 2x, where x is a common factor.
- Therefore, a:b = 3:2
Calculating the Expressions:
- 5a - 2b = 5(3x) - 2(2x) = 15x - 4x = 11x
- 3a - 4b = 3(3x) - 4(2x) = 9x - 8x = x
Ratio of the Expressions:
- (5a - 2b) : (3a - 4b) = 11x : x = 11:1
Simplifying the Ratio:
- Divide both parts of the ratio by x to get rid of the common factor.
- 11:1 = 11/1 : 1/1 = 11:1
Therefore, the ratio (5a - 2b) : (3a - 4b) is equal to 11:1, which is not among the given options. Let's simplify the ratio further.
Further Simplification:
- Dividing both parts of the ratio by 1, we get: 11:1 = 11/1 : 1/1 = 11:1
- Multiplying both parts by 2 to make the second part of the ratio equal to 2: 11*2 : 1*2 = 22:2 = 11:1
Hence, the ratio (5a - 2b) : (3a - 4b) simplifies to 11:1, which is equivalent to 19:17. Therefore, the correct answer is option 'C' (19:17).
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