Final answer:
To solve Olga's equation, 1/4 (1/3k + 9) = 6, we isolated the unknown variable k by applying the distributive property and algebraic manipulation steps, eventually finding k = 45.
Step-by-step explanation:
In order to solve the equation given by the student, Olga, 1/4 (1/3k + 9) = 6, we must perform several steps. Here is a step-by-step guide:
- Identify the unknown, which in this case is k.
- Apply the distributive property by multiplying 1/4 with both terms inside the parentheses: 1/4 × 1/3k + 1/4 × 9 = 6.
- Simplify the left side of the equation: 1/12k + 9/4 = 6.
- Subtract 9/4 from both sides of the equation to isolate the term with the unknown: 1/12k = 6 - 9/4.
- Convert 6 to a fraction with a common denominator with 9/4, which is 4: 1/12k = 24/4 - 9/4.
- Combine the fractions: 1/12k = 15/4.
- Finally, multiply both sides by 12 to solve for k: k = 15/4 × 12, which simplifies to k = 45.
Thus, the solution to Olga's equation is k = 45.