Question

Olga tried to solve an equation step by step. (1)/(4)((1)/(3)k+9)=6 (1)/(3)k+9=24, Step 1 (1)/(3)k=15, Step 2 k=5, Step 3 Find Olga's mistake.

Answer 1

Olga made a mistake by multiplying by 1/4 instead of the inverse 4. The correct value for k should be 45, not 5.

Step-by-step explanation:

Olga's mistake occurred at Step 1 of solving the equation. When she attempted to isolate the term (1/3)k on one side, she incorrectly multiplied 24 by 1/4 instead of correctly multiplying by the inverse of 1/4, which is 4. The correct process after her initial setup would be to multiply both sides of the equation by 4 to eliminate the fraction on the left side, resulting in:

• (1/3)k + 9 = 24
• 4((1/3)k + 9) = 4(24)
• (4/3)k + 36 = 96
• (4/3)k = 96 - 36
• (4/3)k = 60
• k = (3/4)(60)
• k = 45

Therefore, the correct value for k should be 45, not 5.

Answer 2

Olga's mistake occurred in Step 2. Olga incorrectly divided both sides of the equation 1/3k + 9 = 24 by 3.

How to solve equation

Let's solve the given equation step by step:

1/4(1/3)k + 9 = 6

Step 1:

1/3k + 9 = 24

Step 2:

Subtract 9 from both sides:

1/3k = 15

Step 3:

Multiply both sides by 3 to isolate k:

k = 45

So, the correct solution to the equation is k = 45.

The correct procedure would be to subtract 9 from both sides first:

1/3k = 15

Then, multiply both sides by 3 to isolate k.

k = 45

So, the correct solution is k = 45, and the mistake was made in Step 2 where Olga incorrectly divided both sides by 3 instead of subtracting 9 first.