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- Let $x$ and $y$ be two numbers whose sum is $12$ and whose difference is $4$. If $x$ is the smaller number, the correct linear system is $\cdots$?

- $32$ is to be divided into two parts, $x$ and $y$. If $x=\frac{1}{4}y$, the correct linear system is $\cdots$?

- Find two numbers whose sum is $13$ and whose difference is $5$.

- Two numbers add up to $18$. Twice the first number added to the second number gives $27$. The numbers are $\cdots$

- Divide $40$ into two parts, so that one part is two-thirds of the other.

- Divide $100$ into two parts, so that one part is $\frac{9}{16}$ of the other

- The digits of a two-digit number add up to $7$. If the digits are reversed, the number increases by $9$. Find the original number.

- The digits of a two-digit number add up to $10$. If the digits are reversed, the number decreases by $36$. What is the original number?

- A man has $\$5$ notes and $\$10$ notes in his pocket. Altogether, he has $50$ notes that amount to $\$450$. How many of each denomination does he have?

- Divide $72$ into two parts, so that one part is $50\%$ of the other.