a) Solve for $x$.
$$\frac{x+2018}{2019}=\frac{x+2019}{2018}$$
b) Solve for $x$. Give your answers in terms of $a$.
$$\frac{x+a}{a+1}=\frac{x+\left(a+1\right)}{a}$$

Solve for $x$.
$$1-\frac{1}{1-\frac{1}{1-x}}=n$$
Give your answer in terms of $n$.

There is a machine that wraps boxes. 0.5 seconds after the start button is pressed, a box is wrapped. Following that, 1 box is wrapped every 0.5 seconds. In addition, 6 seconds after the start button is pressed, 5 unwrapped boxes enter the machine. Following that, 5 unwrapped boxes enter the machine every 6 seconds. The machine automatically stops once there are no more boxes to wrap. If there are 800 unwrapped boxes in the machine to begin with, the machine will stop $\fbox{$\phantom{682.5}$}$ seconds after the start button is pressed.

$A$ is a 2-digit integer. If the ones digit and the tens digit of $A$ are interchanged, it becomes a 2-digit integer. If this new number is multiplied by $A$, it becomes a multiple of 12. How many possible numbers could $A$ be?

Sachiko leaves her house every morning to go to the train station by bicycle at the same time. If she travels at 16 km/h, she arrives at the station 15 minutes before the train leaves. If she travels at 9.6 km/h, she arrives at the station 15 minutes after the train leaves. What speed should she ride her bicycle at so she arrives at the station 10 minutes before the train leaves?
*Give your answer in km/h.

A store owner ordered 120 items which cost 200 yen each. He puts three items as one set, adds markup and tries to see each set for 1100 yen but he can’t sell them all. He then puts a 20% discount on the remaining sets and sells out. His profit was 5500 yen less than the profit he expected to make at the beginning.
a) How much was the profit he originally expected to make? Give your answer in yen.
b) How many sets did he sell for 1100 yen?

Agnes’s brother, Jiles, left home and walked to a post office that is 1.2 km away to send some letters. 15 minutes after Jiles left, Agnes realized that he forgot one of the letters and chased after him with her bicycle. However, Agnes caught up to her brother after he had already put the letters in the postbox and was on his way home. Jiles walks at a speed of 60 m/min and Agnes rides her bike at a speed of 190 m/min. How many minutes after Agnes left her house did they meet?