How would you write the total money from $x$ small candles if each costs $5? How would you write the total money from $y$ large candles if each costs $12?

Once you have an expression for the money from small candles and another for the money from large candles, how can you combine them to equal the total of $186?

Pick a realistic combination that gives $186, for example $x = 30$ small candles and $y = 3$ large candles (since $30\cdot 5 + 3\cdot 12 = 186$). In Desmos, enter the left-hand side of each choice as a separate expression (for example, 5x + y, x + 12y, 12x + 5y, 5x + 12y), then add sliders for $x$ and $y$ and move them to $x = 30$ and $y = 3$. The expression that evaluates to $186 for those slider values corresponds to the correct equation.

The problem states that $x$ is the number of small candles sold and $y$ is the number of large candles sold.

So:

• $x$ counts small candles.
• $y$ counts large candles.

Each small candle costs $5, and there are $x$ small candles. The total money from small candles is the price times the number:

• Money from small candles: $5x$.

Each large candle costs $12, and there are $y$ large candles. So:

• Money from large candles: $12y$.

The total amount of money collected is the sum of the money from small candles and from large candles, and the problem says that total is $186.

So the correct equation must be:

• (money from small) $+$ (money from large) $=$ (total collected)
• $5x + 12y = 186$

Looking at the choices, this matches option D, so the correct answer is $5x + 12y = 186$.