2.5:150 :: 20:x = ?

Rationale

X = 1200.

To solve the proportion 2.5:150 :: 20:x, we can set up the equation \(\frac{2.5}{150} = \frac{20}{x}\) and cross-multiply to find the value of x, which results in x being equal to 1200.

A (X = 3000) YOUR ANSWER

If x were 3000, then the proportion would not hold true. Substituting back into the equation would yield \(\frac{2.5}{150} \neq \frac{20}{3000}\), as the left side simplifies to \(\frac{1}{60}\) while the right side simplifies to \(\frac{1}{150}\).

B (X = 1000) YOUR ANSWER

Choosing x as 1000 also fails to satisfy the proportion. The equation becomes \(\frac{2.5}{150} \neq \frac{20}{1000}\), as the left side simplifies to \(\frac{1}{60}\) while the right side simplifies to \(\frac{1}{50}\), showing that they are not equal.

C (X = 1500) YOUR ANSWER

If x is 1500, the proportion still does not hold. The equation would be \(\frac{2.5}{150} \neq \frac{20}{1500}\). The left side simplifies to \(\frac{1}{60}\), while the right side simplifies to \(\frac{1}{75}\), indicating a mismatch.

D (X = 1200) CORRECT

When substituting x = 1200 into the equation, we have \(\frac{2.5}{150} = \frac{20}{1200}\). Both sides simplify to \(\frac{1}{60}\), confirming that the proportion is valid.

Conclusion

In solving the proportion 2.5:150 :: 20:x, we find that x must equal 1200 to maintain equality. This solution effectively demonstrates the method of cross-multiplying to evaluate proportional relationships, verifying that only the choice of x = 1200 satisfies the equation. All other options yield unequal ratios, illustrating the importance of accurate calculations in proportional reasoning.

2.5:150 :: 20:x = ?

X = 1200.

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