Use the wax amounts ($0.5$ lb and $0.8$ lb) to write one equation, and the burn times (30 hours and 50 hours) to write another equation, each equal to the given total.

Consider multiplying or dividing the equations so that the coefficients are whole numbers, and then use substitution or elimination to solve the system.

The question asks for the number of deluxe candles, so once you have an equation in one variable, make sure you solve for $d$ and check that it fits both the wax and burn-time conditions.

In Desmos, type the two equations as

• 0.5x + 0.8y = 32
• 30x + 50y = 1950 Use x for the number of standard candles and y for the number of deluxe candles.

Look at the graph where the two lines intersect, or click on the intersection point that Desmos highlights. The coordinates will appear as $(x, y)$.

Use the $y$-coordinate of the intersection point (the value of $y$) as the number of deluxe candles. Compare this value with the answer choices.

Let:

• $s$ = number of standard candles
• $d$ = number of deluxe candles

Use the information in the problem to create two equations:

• Wax used: each standard uses $0.5$ lb and each deluxe uses $0.8$ lb, for a total of $32$ lb:

• Burn time: each standard burns $30$ hours and each deluxe burns $50$ hours, for a total of $1{,}950$ hours:

Now you have a system of two equations in $s$ and $d$.

Rewrite the equations with integer coefficients:

• Multiply the wax equation by $10$ to eliminate decimals:

• Divide the burn-time equation by $10$ to simplify it:

So the system becomes:

Eliminate $s$ by making the $s$-coefficients opposites.

• Multiply the first equation by $3$:

• Multiply the second equation by $-5$:

Add these two new equations:

Now you have a single equation involving only $d$.

From the equation

solve for $d$ by dividing both sides by $-1$:

This means the artisan made $15$ deluxe candles.

So the correct answer is C) 15.