A7. If we paid a quarter of the debt, then half of the remainder, and an additional 5400 euros, the entire debt would be settled. How many euros are we in debt?
(A) 5400
(B) 9450
(C) 10800
(D) 14400
(E) 21600
A7. Let the debt be denoted by $x$ and write the equation $x=\frac{1}{4} x+\frac{3}{8} x+5400$. The debt is $x=14400$ euros. We can conclude differently: if we paid a quarter of the debt and then half of the remainder, the amount of 5400 euros would represent exactly half of the remainder, $5400+5400=10800$ euros is three quarters of the total debt. The total debt is $10800+\frac{1}{3} \cdot 10800=10800+3600=14400$ euros.