Step 1 :The standard food cost of a steak dinner is \$4.50.
Step 2 :The desired food cost percentage is 34 percent or 0.34 in decimal form.
Step 3 :The base selling price can be calculated by dividing the standard food cost by the desired food cost percentage.
Step 4 :Using the formula, the base selling price is calculated as \(\frac{4.5}{0.34} = 13.235294117647058\).
Step 5 :Rounding to the nearest cent, the base selling price is approximately \$13.24.
Step 6 :Final Answer: The base selling price using the ingredients mark-up method would be \(\boxed{13.24}\).