There are 2 hotels, Hotel Duxton and Hotel Supreme. There were 219 more guests in Hotel Duxton than in Hotel Supreme. After 57 guests had le

There are 2 hotels, Hotel Duxton and Hotel Supreme. There were 219 more guests in Hotel Duxton than in Hotel Supreme. After 57 guests had left Hotel Supreme, the number of guests in Hotel Duxton became 4 times the number of guests in Hotel Supreme. How many guests are left at Hotel Supreme?

d = Hotel Duxton       s = Hotel Supreme

(1) $$d-s = 219$$

(2) $$s_1 = s - 57$$

(3)$$d - s_1 = 219 + 57 = 276$$

(4) $$d = 4\cdot s_1$$

put (4) into (3):

$$\begin{array}{rcl}
4\cdot s_1 -s_1 &=& 276\\
3\cdot s_1 &=& 276 \\
s_1 &=& 92
\end{array}$$

$$\text{\small{
\begin{array}{lrclr}
& Hotel Duxton & Hotel Supreme \\
bevor & 368 = 149 + 219 & 92 + 57 = 149 \\
after & 368 = 92\cdot 4 & 92\\
\end{array}
}}$$