Step 1 :First, we need to convert the child's weight from pounds to kilograms, since the dosage is given in mg/kg. We know that 1 pound is approximately 0.453592 kg, so a child weighing 53 pounds weighs approximately \(53 \times 0.453592 = 24.04\) kg.
Step 2 :Next, we calculate the total dosage for the child. The doctor has ordered 6 mg/kg, so the total dosage is \(6 \times 24.04 = 144.24\) mg.
Step 3 :Finally, we need to determine how many tablets this corresponds to. Each tablet contains 400 mg of theophylline anhydrous, so the child should be administered \(\frac{144.24}{400} = 0.36\) tablets.
Step 4 :However, it's not practical to administer 0.36 of a tablet. Therefore, the child should be administered \(\boxed{1}\) tablet, and the dosage should be adjusted as necessary under the guidance of the pediatrician.