Ratio and Proportion: 15:1000 :: X:100

Rationale

X = 1.5

To solve for X in the proportion 15:1000 :: X:100, we can set up a cross-multiplication which reveals that X must equal 1.5 to maintain the same ratio.

A (X = 7.5) YOUR ANSWER

If X were 7.5, we would compute the ratio as 15:1000 = 7.5:100. Cross-multiplying gives 15 * 100 = 7.5 * 1000, which simplifies to 1500 = 7500. This equation is not true, indicating that 7.5 does not maintain the correct ratio.

B (X = 6,666) YOUR ANSWER

Substituting X with 6,666 results in a ratio of 15:1000 = 6,666:100. Upon cross-multiplication, we find 15 * 100 = 6,666 * 1000, leading to 1500 = 6,666,000. This clearly shows that 6,666 does not satisfy the proportion.

C (X = 0.15) YOUR ANSWER

If we set X to 0.15, the ratio becomes 15:1000 = 0.15:100. Cross-multiplying yields 15 * 100 = 0.15 * 1000, which gives 1500 = 150. This result indicates that 0.15 is not correct, as it does not keep the ratios equal.

D (X = 1.5) CORRECT

Using X = 1.5, we have the ratio 15:1000 = 1.5:100. Cross-multiplying gives 15 * 100 = 1.5 * 1000, leading to 1500 = 1500, which is a true statement. Therefore, this value correctly maintains the ratio.

Conclusion

In the given proportion, the value of X that maintains the ratio consistent with 15:1000 is 1.5. Other choices do not satisfy the proportion, which is verified through cross-multiplication. Thus, understanding ratios and proportions allows us to find the correct value of X in such cases.

Ratio and Proportion: 15:1000 :: X:100

X = 1.5

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