Step 1 :The problem is asking for the amount of oil needed to make 35 ounces of salad dressing. The ratio of oil to vinegar is 5:2. This means that for every 7 ounces of salad dressing (5 ounces of oil + 2 ounces of vinegar), 5 ounces of oil are used.
Step 2 :To find out how much oil is needed for 35 ounces of salad dressing, we need to set up a proportion and solve for the unknown.
Step 3 :First, we calculate the ratio of oil in the total dressing, which is \(\frac{5}{5+2} = 0.7142857142857143\).
Step 4 :Then, we multiply this ratio by the total amount of dressing needed, which is \(0.7142857142857143 \times 35 = 25.0\).
Step 5 :So, the restaurant will need 25 ounces of oil to make 35 ounces of salad dressing.
Step 6 :Final Answer: \(\boxed{25}\)