Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

At a historical landmark, candles are used to simulate an authentic atmosphere. A volunteer is currently putting new candles in the candle holders. On the east side, he replaced candles in 8 small candle holders and 11 large candle holders, using a total of 87 candles. On the west side, he replaced the candles in 8 small candle holders and 15 large candle holders, for a total of 107 candles. How many candles does each candle holder hold?

Each small candleholder holds how many candles, and each large one holds how many
candles.

Answer 1

Let's define the number of candles in each type of holder.

Let \( x \) be the number of candles that a small candle holder holds, and let \( y \) be the number of candles that a large candle holder holds.

We can now set up the system of equations based on the information given.

From the east side:

\[
8x + 11y = 87 \quad \text{(1)}
\]

From the west side:

\[
8x + 15y = 107 \quad \text{(2)}
\]

Now we will solve this system of equations. First, we can eliminate \( x \) by subtracting equation (1) from equation (2).

\[
(8x + 15y) - (8x + 11y) = 107 - 87
\]

This simplifies to:

\[
4y = 20 \quad \text{(3)}
\]

Now we can solve for \( y \):

\[
y = \frac{20}{4} = 5
\]

Now that we have \( y \), we can substitute it back into either equation (1) or (2) to find \( x \). Let's use equation (1):

\[
8x + 11(5) = 87
\]

This simplifies to:

\[
8x + 55 = 87
\]

Subtracting 55 from both sides gives:

\[
8x = 32
\]

Now divide both sides by 8:

\[
x = 4
\]

Now we have the values:

- Each small candle holder holds \( x = 4 \) candles.
- Each large candle holder holds \( y = 5 \) candles.

**Final Answers:**

Each small candleholder holds **4** candles, and each large one holds **5** candles.