Step 1 :First, we need to find the cost per pound of steak at grocery store 2. We can use the given data in the table to find the cost per pound for each weight.
Step 2 :For 2 pounds: \(\frac{15}{2} = 7.50\) dollars per pound
Step 3 :For 3 pounds: \(\frac{22.50}{3} = 7.50\) dollars per pound
Step 4 :For 5 pounds: \(\frac{37.50}{5} = 7.50\) dollars per pound
Step 5 :For 9 pounds: \(\frac{67.50}{9} = 7.50\) dollars per pound
Step 6 :Now we know that the cost per pound of steak at grocery store 2 is \(7.50\) dollars.
Step 7 :Next, we need to find the weight of steak that has the same cost in both grocery stores.
Step 8 :Let's set the cost of steak at grocery store 1 equal to the cost of steak at grocery store 2: \(6.75x = 7.50x\)
Step 9 :Now, we can solve for x: \(\frac{6.75}{7.50} = x\)
Step 10 :Calculating x, we get: \(x \approx 0.90\)
Step 11 :So, the weight of steak that has the same cost in both grocery stores is approximately \(\boxed{0.90}\) pounds.