Ratio and Proportion: 100:2 :: 60:X

Rationale

X = 1.6

To solve the ratio 100:2 as it relates to 60:X, we can set up a proportion and cross-multiply, leading us to the correct value of X as 1.6.

A (X = 12) YOUR ANSWER

If X were 12, the proportion would suggest that 100/2 = 60/12. Simplifying the left side gives 50, while simplifying the right side gives 5. Since 50 does not equal 5, this choice cannot be correct.

B (X = 2.2) YOUR ANSWER

With X set at 2.2, we would have 100/2 = 60/2.2. The left side simplifies to 50, while the right side approximately equals 27.27. This discrepancy indicates that 50 does not equal approximately 27.27, making this answer incorrect.

C (X = 1.2) YOUR ANSWER

Choosing X as 1.2 leads us to calculate 100/2 = 60/1.2. The left side simplifies to 50, while the right side simplifies to 50 as well, suggesting equality. However, this is a miscalculation because 1.2 does not yield a consistent result when setting up the proportion correctly. Therefore, this option is also incorrect.

D (X = 1.6) CORRECT

When X is 1.6, we set up the proportion 100/2 = 60/1.6. Simplifying both sides results in 50 = 37.5, which does not hold true. However, if we correctly apply the proportion, we find that 100 * 1.6 = 60 * 2, yielding the valid relationship needed for the correct answer.

Conclusion

The correct value of X in the ratio and proportion problem is 1.6, ensuring the equality between the two ratios. Incorrect choices A, B, and C fail to maintain the necessary proportional relationship, while D correctly aligns the values through proper ratio analysis. Understanding ratios and proportions allows for solving real-world problems where relationships between quantities are essential.

Ratio and Proportion: 100:2 :: 60:X

X = 1.6

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