Ratio and Proportion: 0.9: X:: 15:90

Ratio and Proportion: 0.9: X:: 15:90

A.
X=7.4

B.
X=1.6

C.
X=5.4

D.
X=3.6

The Correct Answer and Explanation is:

To solve the proportion ( 0.9 : X :: 15 : 90 ), we need to set up an equation using the property of proportions. A proportion states that two ratios are equal, which can be written as:

[
\frac{0.9}{X} = \frac{15}{90}
]

Now, follow these steps to find the value of ( X ).

Step 1: Simplify the second ratio

Simplify ( \frac{15}{90} ):
[
\frac{15}{90} = \frac{1}{6}
]

Thus, the equation becomes:
[
\frac{0.9}{X} = \frac{1}{6}
]

Step 2: Cross-multiply

To eliminate the fractions, we cross-multiply. This means multiplying the numerator of one fraction by the denominator of the other:

[
0.9 \times 6 = 1 \times X
]

This simplifies to:
[
5.4 = X
]

Step 3: Conclusion

The value of ( X ) is 5.4.

Verification:

To ensure the solution is correct, check whether the original ratios are equivalent when ( X = 5.4 ). The original proportion is:

[
\frac{0.9}{5.4} = \frac{15}{90}
]

Simplifying ( \frac{0.9}{5.4} ):
[
\frac{0.9}{5.4} = \frac{1}{6}
]

Since both ratios equal ( \frac{1}{6} ), the proportion holds true, confirming that ( X = 5.4 ) is correct.

Answer:

The correct answer is C. X = 5.4.

Explanation:

This problem demonstrates how to use the concept of cross-multiplication to solve proportions. Proportions are a way to express the equality between two ratios, and cross-multiplying helps simplify the equation. By equating the products of the extremes and the means, we can solve for the unknown variable. This method is commonly used in various mathematical and real-world applications, such as scaling recipes, working with maps, and financial calculations.