Given two numbers where adding 40% of the initial number to the second causes the second number to rise to five-fourths of its value, find the proportion between the initial and second numbers?
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Answer: D. 5 : 8
Explanation
Adding 40 percent of the initial number to the second number equates to five-fourths of the second number. Rearranging this algebraic relationship isolates the ratio of the initial number to the second number. Simplifying the resulting fraction produces the correct final proportion of 5 to 8. Proportions express the relative magnitude of two quantities as a ratio of one to another. Algebraic word problems translate descriptive English statements into mathematical equations involving unknown variables. Fractions and percentages can be used interchangeably when setting up proportional growth equations.
Economic models frequently use proportional relationships to describe interactions between different market variables. Mixture and solution problems in chemistry rely on setting up accurate algebraic proportions between components. This type of problem tests the ability to translate complex verbal conditions into clean mathematical ratios. Option A inverts the correct ratio terms, representing the inverse proportion instead of the requested order. Option B represents a reversed fraction that misidentifies which quantity serves as the numerator. Option C uses incorrect coefficients that fail to satisfy the balance of the stated algebraic condition.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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