A cinema sells adult tickets at 50 thousand dong and child tickets at 20 thousand dong, taking 2 million dong in total. Writing x for the number of adults and y for the number of children, write the first-degree equation in two unknowns and give one solution in whole numbers.

Step-by-step solution

1. 1

   Get every quantity into the same units before writing anything. Prices are in thousands of dong and the total is in millions, so convert the total: $2$ million dong $=2000$ thousand dong. Mixing the two units is the only real difficulty in this problem.

2. 2

   Build the revenue expression. $x$ adults at $50$ thousand each bring in $50x$; $y$ children at $20$ thousand each bring in $20y$. Their sum is the takings:

   $50x+20y=2000.$

   That is the required first-degree (linear) equation in two unknowns.

3. 3

   Simplify by the common factor. All three coefficients are divisible by $10$:

   $5x+2y=200.$

   Smaller numbers make it much easier to hunt for whole-number solutions.

4. 4

   Find one whole-number solution. Solve for $y$:

   $y=\frac{200-5x}{2}.$

   For $y$ to be a whole number, $200-5x$ must be even, which happens exactly when $x$ is even. Taking $x=20$ gives

   $y=\frac{200-100}{2}=50.$

5. 5

   Check the pair against the original wording. $20$ adults pay $20\times 50=1000$ thousand dong and $50$ children pay $50\times 20=1000$ thousand dong; together $2000$ thousand $=2$ million dong ✓.

6. 6

   Note that many solutions exist. Because one equation cannot pin down two unknowns, the solutions form a family: $x$ any even number from $0$ to $40$, with $y=\tfrac{200-5x}{2}$. For instance $(0,100)$, $(20,50)$ and $(40,0)$ all work. The problem asks for only one, which is why it says 'give one solution'.