Question

Ross needs to have a procedure done, and since he is over 65 he is on Medicare. Medicare says that according to their plan the allowed amount is 7/ 8 of what the doctors office charges. Of that allowed amount they will pay 3 /4 and Ross will be out of pocket 1 /4 . If Ross had to pay $262.50, how much did the office want to charge for the procedure?
USA Test Prep Answer is X=$1,200

Answer 1

Answer:

$\large \boxed{\ 1200.00}$

Step-by-step explanation:

              Let the office charge  = x

     Amount paid by Medicare = ⅞x

Amount paid by Ross = ¼(⅞x) = $262.50

 

Solve for x

$\begin{array}{rcrl}\dfrac{1}{4} \left(\dfrac{7}{8}x \right ) & = & \ 262.50 & \\\dfrac{7}{32}x & = & \ 262.50 & \text{Multiplied the fractions}\\\\7x & = & \ 8400.00 & \text{Multiplied each side by 32}\\x & = & \mathbf{\ 1200.00} & \text{Divided each side by 7}\\\end{array}\\\text{The office wanted to charge } \large \boxed{\mathbf{\ 1200.00}}$

Check:

$\begin{array}{rcl}\dfrac{1}{4} \left(\dfrac{7}{8}\times \ 1200.00 \right ) & = & \ 262.50\\\\\dfrac{1}{4} \left(\ 1050.00 \right ) & = & \ 262.50\\\\\ 262.50 & = & \ 262.50\\\end{array}$

OK.