The sum of the cubes of two numbers is 280, and their ratio is 2:3. Find the smaller number.
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Answer: A. 4
Explanation
Representing the two numbers as algebraic multiples of two and three gives expressions containing a common variable. Summing the cubes of these expressions results in a total equation equal to thirty-five times the cubed variable. Dividing the total sum by thirty-five gives eight, making the variable two and the smaller number equal to four. Cubes of algebraic terms are calculated by raising both the numerical coefficient and the variable to the third power. Ratio problems allow unknown values to be expressed using a shared scaling variable to simplify complex equations. Solving cubic equations often involves simplifying coefficients before taking the cube root of both sides.
Option B represents the larger number in the ratio rather than the smaller number requested by the question. Option C fails to satisfy the cubic sum equation when substituted back into the original problem statement. Option D produces a sum of cubes that falls well short of the target value of two hundred eighty.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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