Question 3

y is equal to 32 1/3

To determine the value of y, which is positioned three times as far from 10 as it is from 40, we calculate based on the distances involved and find that y equals 32 1/3.

A) 31.66666667

This option is incorrect because it does not satisfy the condition of being three times as far from 10 compared to its distance from 40. When evaluated, the ratio of distances does not align with the specified relationship.

B) 32

While 32 is close, it does not fulfill the requirement of being three times as far from 10 as it is from 40. The calculations reveal that the distances do not maintain the specified ratio, thus rendering this choice incorrect.

C) 32 1/3

This is the correct answer. When y is set to 32 1/3, the distances from 10 and 40 are calculated as follows: The distance from 10 is 22 1/3, and the distance from 40 is 7 2/3. The ratio of these distances confirms that y is indeed three times farther from 10 than from 40.

D) 32.5

This option is incorrect because the distance from 10 would be 22.5 and from 40 would be 7.5, which does not satisfy the condition that the distance from 10 must be three times the distance from 40. Thus, this choice fails to meet the criteria.

E) 33

Although 33 is close to the correct answer, it fails to satisfy the distance criteria set forth in the problem. The computed distances from 10 and 40 do not maintain the necessary ratio, leading to its inaccuracy.

Conclusion

The correct answer, 32 1/3, meets the established condition of distance between the points on the number line. Each of the other options fails to achieve the required ratio of being three times as far from 10 compared to the distance from 40, confirming that they do not represent the solution accurately.