What is the missing value in the ratio and proportion 15:2000::x:200?

Rationale

1.5

To find the missing value in the proportion 15:2000::x:200, we can set up the equation \(\frac{15}{2000} = \frac{x}{200}\). Solving for \(x\) gives us the result of 1.5.

A (1.5) CORRECT

This choice is the correct answer. By cross-multiplying the proportion, we have \(15 \times 200 = 2000 \times x\), which simplifies to \(x = \frac{15 \times 200}{2000} = 1.5\).

B (7.777) YOUR ANSWER

This choice is incorrect because substituting 7.777 into the proportion does not satisfy the equality. If we calculate using this value, we find that \(\frac{15}{2000} \neq \frac{7.777}{200}\), leading to inconsistent ratios.

C (0.15) YOUR ANSWER

Choosing 0.15 results in an incorrect ratio as well. When substituted into the proportion, it leads to \(\frac{15}{2000} \neq \frac{0.15}{200}\). The calculations show that 0.15 is significantly smaller than the value needed to maintain the proportion.

D (15) YOUR ANSWER

This option is also incorrect because substituting 15 into the proportion yields \(\frac{15}{2000} \neq \frac{15}{200}\). The ratio of the terms would not balance, since 15 represents the original numerator rather than the missing value.

Conclusion

In the given ratio and proportion, the correct value for \(x\) is 1.5, derived from the relationship defined by the cross-multiplication of the proportion. The other choices do not satisfy the conditions of the proportion, demonstrating that only 1.5 maintains the equality necessary for the ratios to be equivalent.

What is the missing value in the ratio and proportion 15:2000::x:200?

1.5

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