Ratio and Proportion 15:1000::x:100 = ?

Rationale

x = 1

To solve the proportion 15:1000::x:100, we can set up the equation 15/1000 = x/100. Cross-multiplying gives us 15 * 100 = 1000 * x, which simplifies to x = 1.

A (1.5) YOUR ANSWER

If we substitute x = 1.5 into the proportion, we would find that 15:1000::1.5:100 does not hold true. Specifically, 1.5/100 would simplify to 0.015, whereas 15/1000 simplifies to 0.015 as well, making this choice invalid for maintaining the equality.

B (2) YOUR ANSWER

Substituting x = 2 leads to 15:1000::2:100, which simplifies to 2/100 or 0.02. However, 15/1000 simplifies to 0.015, indicating that these ratios do not match, thus this choice is incorrect.

C (1) CORRECT

This choice correctly satisfies the equation. When x = 1, the proportions become 15:1000::1:100, which simplifies to 0.015 on both sides, confirming the equality of the ratios. Therefore, this is the correct answer.

D (1.2) YOUR ANSWER

If we take x = 1.2, the proportion becomes 15:1000::1.2:100. This simplifies to 1.2/100 or 0.012, which does not equal 15/1000 or 0.015. Hence, this choice is not valid.

Conclusion

In solving the proportion 15:1000::x:100, the value of x that maintains the equality is 1. This is confirmed through cross-multiplication, where only x = 1 satisfies the condition of equivalent ratios. Other choices either yield mismatched ratios or fail to maintain equality, highlighting the importance of precise calculations in ratio and proportion problems.

Ratio and Proportion 15:1000::x:100 = ?

x = 1

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