Two numbers in a 2 : 3 ratio have an L.C.M of 48. What is their sum_________?
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Answer: C. 40
Explanation
Representing two numbers in a two to three ratio as two x and three x helps find their LCM. The least common multiple of these proportional terms equals six x which is set to forty eight. Solving for x gives eight making the numbers sixteen and twenty four whose sum is forty. The least common multiple of proportional terms incorporates both the common multiplier and ratio factors. Summing two numbers requires determining their exact individual values first through algebraic solving. Proportional ratios define relative magnitudes while variable multipliers set absolute values.
Number theory problems involving ratios and LCM help develop fundamental algebraic problem-solving skills. Synchronizing cyclical events often relies on finding least common multiples in practical scheduling. Proportional scaling is widely used in chemistry and recipe formulation to maintain ingredient ratios. Option A suggests twenty eight which is too small to satisfy the given LCM condition. Option B suggests thirty two which fails to yield the correct least common multiple. Option D suggests sixty four which overstates the sum of the derived number values.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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