Let the cost of a large candle be $x$ and the cost of a small candle be $y$.

Given:

• Lexi bought 2 large candles and 5 small candles for $30. This gives us the equation: $2x + 5y = 30$
• Carl bought 1 large candle and 3 small candles for $16.75. This gives us the equation: $x + 3y = 16.75$

Step 1: Solve the system of equations

We have the system:

1. $2x + 5y = 30$
2. $x + 3y = 16.75$

To solve for $x$ and $y$, we can use substitution or elimination. Let's use substitution.

From the second equation: $x = 16.75 - 3y$

Step 2: Substitute $x$ into the first equation

Substitute $x = 16.75 - 3y$ into the first equation: $2(16.75 - 3y) + 5y = 30$

Expand: $33.5 - 6y + 5y = 30$

Simplify: $33.5 - y = 30$

Step 3: Solve for $y$

$-y = 30 - 33.5$ $-y = -3.5$ $y = 3.5$

Step 4: Substitute $y = 3.5$ back into the second equation to find $x$

Now substitute $y = 3.5$ into the equation $x + 3y = 16.75$: $x + 3(3.5) = 16.75$ $x + 10.5 = 16.75$ $x = 16.75 - 10.5$ $x = 6.25$

Conclusion:

• The cost of a large candle is $\boxed{6.25}$ dollars.
• The cost of a small candle is $\boxed{3.5}$ dollars.

Would you like more details or have any questions on this? Here are some related questions for further exploration:

1. How can you solve a system of equations using the elimination method?
2. How does substitution compare to elimination in solving word problems?
3. What happens if you solve a system of equations with more than two variables?
4. How can you check if the values for $x$ and $y$ are correct?
5. What real-world problems can systems of equations model other than shopping scenarios?

Tip: Always try to simplify your equations as much as possible before proceeding with solving!