Question 1

A is 5 less than 6 × C.

To determine the relationship between A and C, we can express A in terms of C using the given relationships. Since A is three times B and B is five less than twice C, we find that A equals 6 times C minus 5.

A) A is 15 less than 6 × C.

This statement is incorrect because it suggests that A is 15 units less than 6 times C, while our calculations show that A is 5 less than 6 times C, not 15.

B) A is 15 less than 5 × C.

This option is also incorrect. Based on the relationship derived, A does not equate to being 15 less than 5 times C, as the derived expressions indicate a different relationship.

C) A is 10 less than 5 × C.

This statement is incorrect as well. The relationship derived from the equations shows that A does not have a difference of 10 from 5 times C; rather, it is structured around a different factor altogether.

D) A is 5 less than 6 × C.

This statement accurately describes the relationship between A and C. Through the calculations, we see that A, expressed as 3B, directly translates to being 5 units less than 6 times C after substituting B with its expression in terms of C.

E) A is 5 less than 5 × C.

This statement is incorrect. The calculations reveal that A is not 5 less than 5 times C; instead, it is specifically 5 less than 6 times C, indicating a different relationship.

Conclusion

The correct answer, D, clearly articulates the relationship between A and C, as established through the equations provided. All other options fail to accurately reflect the derived relationship, either overstating or understating the difference between A and C based on the correct mathematical interpretations.