A bag has $x$ five-cent coins and $y$ ten-cent coins. Altogether, there are $130$ coins in the bag. Write down an equation, in terms of $x$ and $y$, for the total number of coins in the bag.
The combined value of the coins in the bag is $\$8.15$. Write down an equation, in terms of $x$ and $y$, for the total value of the coins in the bag.
Use the two simultaneous equations to determine how many of each type of coin are in the bag. Show your working.
A machine produces five-cent coins. It produces $720$ coins each minute. The machine runs for $24$ hours per day. Calculate the total value, in dollars, of the coins produced by the machine in $300$ days. Give your answer in standard form, correct to $3$ significant figures.
The diameter of a five-cent coin is $21.2\text{ mm}$, correct to the nearest $0.1\text{ mm}$. The diameter of a ten-cent coin is $17.9\text{ mm}$, correct to the nearest $0.1\text{ mm}$. Marlon arranges $10$ five-cent coins in a line and $10$ ten-cent coins in a line. Calculate the upper bound of the difference between the lengths of the two lines.