Ratio and Proportion: 240 : X :: 80 : 0.8 (Enter a numeric value only.)

Rationale

2.4

To solve the proportion 240 : X :: 80 : 0.8, we can use cross-multiplication, which gives us 240 * 0.8 = 80 * X. Simplifying this equation leads us to find that X equals 2.4.

A (2.4) CORRECT

This value is derived from the proportion by cross-multiplying and simplifying the equation as mentioned. Specifically, 240 multiplied by 0.8 equals 192, and dividing that by 80 results in 2.4. Therefore, this is the correct answer.

B (3.2) YOUR ANSWER

Choosing 3.2 would suggest that 240 : 3.2 is equivalent to 80 : 0.8. However, if we check with cross-multiplication, we find that 240 * 0.8 equals 192, while 80 * 3.2 equals 256. Since these products do not match, 3.2 cannot be the correct answer.

C (4) YOUR ANSWER

If we consider 4 as the value for X, we would calculate 240 : 4 and find that 80 : 0.8 should yield similar products. Cross-multiplying shows 240 * 0.8 equals 192, while 80 * 4 equals 320. The mismatch in these results confirms that 4 is incorrect.

D (1.6) YOUR ANSWER

Selecting 1.6 for X would lead to a similar contradiction. Cross-multiplying 240 and 0.8 gives 192, while 80 multiplied by 1.6 equals 128. Thus, 1.6 does not satisfy the proportion, indicating it is not the right choice.

Conclusion

The correct answer is 2.4, which satisfies the proportion through proper cross-multiplication. The other options fail to maintain the equality required by the ratio and proportion statement due to mismatched products in their calculations. Understanding how to manipulate proportions is crucial for solving similar mathematical problems effectively.

Ratio and Proportion: 240 : X :: 80 : 0.8 (Enter a numeric value only.)

2.4

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