Numbers a and b are in a 3:5 ratio. Adding 2 to both changes the ratio to 2:3. Find b.
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Answer: B. 10
Explanation
Letting the numbers be three x and five x establishes an algebraic ratio expression matching the problem statement. Adding two to both quantities creates the equation three x plus two over five x plus two equal to two-thirds. Cross-multiplying and solving the linear equation reveals x equals two, making b equal to five times two or ten. Ratio variables can be represented using an unknown multiplier to set up algebraic equations for unknown quantities. Cross multiplication is a standard algebraic technique used to solve fractional proportion equations quickly. Linear equations allow for the exact determination of unknown scaling factors when given shifted ratio conditions.
Option A gives fifteen, which produces incorrect ratios when two is added to both numerator and denominator. Option C gives eight, failing to satisfy the simultaneous algebraic conditions established by the problem. Option D gives five, which yields an incorrect proportion when tested against the shifted ratio values.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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