A is 3 × B, and B is 5 less than 2 × C. Which of the following statements describes the relationship between A and C?

Rationale

A is 5 less than 6 × C.

To find the relationship between A and C, we can express A in terms of C using the equations provided. Given that A = 3 × B and B = 2 × C - 5, substituting B into the equation for A yields A = 3(2 × C - 5) = 6 × C - 15. Thus, A can be rewritten as A = 6 × C - 15, which means A is indeed 5 less than 6 × C.

A (A is 15 less than 6 × C.) YOUR ANSWER

This statement is incorrect because it suggests that A = 6 × C - 15, which is true, but it misrepresents the relationship as it does not account for the additional 5 units. The correct expression shows A = 6 × C - 15, indicating a difference of 15 rather than 5.

B (A is 15 less than 5 × C.) YOUR ANSWER

This choice is incorrect because the expression implies A = 5 × C - 15. However, substituting the values derived from the initial equations does not yield this result. In fact, A is related to 6 × C, not 5 × C.

C (A is 10 less than 5 × C.) YOUR ANSWER

This option incorrectly states that A = 5 × C - 10. The calculations based on the relationships between A, B, and C do not support this equation, as the relationship involves 6 × C rather than 5 × C.

D (A is 5 less than 6 × C.) CORRECT

This statement correctly describes the relationship derived from the equations, as it accurately reflects how A can be expressed in relation to C. The equation A = 6 × C - 15 simplifies to show that A is indeed 5 less than 6 × C.

E (A is 5 less than 5 × C.) YOUR ANSWER

This choice is incorrect since it states A = 5 × C - 5. The derived relationship indicates that A is related to 6 × C and not to 5 × C, making this option inconsistent with the established equations.

Conclusion

The relationship between A and C can be accurately described as A being 5 less than 6 × C. This is derived from substituting B's equation into A's equation, confirming that A's value is tied to the coefficient of 6 for C, with an adjustment of -15, thus establishing the correct relationship.

A is 3 × B, and B is 5 less than 2 × C. Which of the following statements describes the relationship between A and C?

A is 5 less than 6 × C.

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