Ratio and proportion: 0.8:10 :: x:100

Rationale

x = 8.

To solve the proportion 0.8:10 :: x:100, we can cross-multiply. This results in 0.8 * 100 = 10 * x, simplifying to 80 = 10x, leading to x = 8.

A (x = 0.8) YOUR ANSWER

This choice suggests that x is equal to 0.8, which does not maintain the ratio given in the original proportion. If x were 0.8, the relationship would not hold true when comparing to the value of 100, as 0.8 would not be proportionally equivalent with 10.

B (x = 80) YOUR ANSWER

Choosing x = 80 would imply that the ratio is 0.8:10 :: 80:100. However, when we check the cross-multiplication, 0.8 * 100 (which equals 80) does equal 10 * 80, indicating that this choice would also incorrectly represent the original proportion since it does not solve the ratio correctly.

C (x = 800) YOUR ANSWER

This option suggests that x is equal to 800. This would imply a significantly larger number in the proportion, making the relationship invalid. Cross-multiplying would yield 0.8 * 100 = 10 * 800, resulting in 80 = 8000, which is clearly incorrect.

D (x = 8) CORRECT

This is the correct answer. When substituting x = 8, the proportion holds true: 0.8:10 :: 8:100. Cross-multiplying gives us 0.8 * 100 = 80 and 10 * 8 = 80, confirming that both sides of the equation are equal.

Conclusion

To maintain the integrity of the ratio and proportion, the correct value of x that satisfies the relationship 0.8:10 :: x:100 is 8. This conclusion is validated through cross-multiplication, confirming that the mathematical relationship holds true. All other choices fail to preserve the proportional integrity of the original statement.

Ratio and proportion: 0.8:10 :: x:100

x = 8.

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