Final answer:
The student's Mathematics problem involves finding the expression for c in terms of a. The correct expression, based on the relation '8 less than a is 6 more than c,' is c = a - 14, which is not listed among the provided options. The correct expression for c in terms of a would be c = a - 14.
Step-by-step explanation:
The student's question relates to the field of Mathematics, specifically to algebraic expressions. The problem can be set up as an equation based on the given statement '8 less than a is 6 more than c.' Let's solve the given puzzle step by step. 1. "8 less than a" means we take the number a and subtract 8 from it. In mathematical terms, this is expressed as: a - 8 2. "6 more than c" means we add 6 to the number c.
In mathematical terms, this is expressed as: c + 6 3. The statement tells us that these two expressions are equal. This gives us the equation: a - 8 = c + 6 4. We want to express c in terms of a, so we need to solve the equation for c. To do this, we isolate the variable c on one side of the equation. We can start by moving the constant term +6 from the right side to the left side.
This is done by subtracting 6 from both sides of the equation: a - 8 - 6 = c 5. Combine the numeric terms on the left side: a - 14 = c We now have c expressed in terms of a. The expression c = a - 14 describes the relationship between a and c as per the statement provided. Comparing our expression to the given choices: a) c = a + 2 (Incorrect) b) c = a − 2 (Incorrect) c) c = a + 6 (Incorrect) d) c = a − 6 (Incorrect) None of the choices exactly matches our derived expression c = a - 14.
However, we need to select the best available option from the provided choices. Since none of the given options is correct, and without any further context, it would not be possible to definitively choose one of the incorrect options. There might be an error in the provided choices. Under usual circumstances, you'd likely want to alert whoever provided the question that there appears to be a mistake in the answer choices.This translates to:
a - 8 = c + 6
To express c in terms of a, we isolate c:
c = (a - 8) - 6
c = a - 14
Therefore, none of the options given a) c = a + 2, b) c = a - 2, c) c = a + 6, or d) c = a - 6 are correct. The correct expression for c in terms of a would be c = a - 14.