Question

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 25 small candle holders and 16 large candle holders, using a total of 203 candles. On the west side, he replaced the candles in 3 small candle holders and 16 large candle holders, for a total of 137 candles. How many candles does each candle holder hold?

Answer 1

Let x be the number of candles in a small candle holder

Let y be the number of candles in a large candle holder

On the east side, he replaced candles in 25 small candle holders and 16 large candle holders, using a total of 203 candles:

$25x+16y=203$

On the west side, he replaced the candles in 3 small candle holders and 16 large candle holders, for a total of 137 candles:

$3x+16y=137$

System of equations:

$\begin{gathered} 25x+16y=203 \\ 3x+16y=137 \end{gathered}$

Elimination method:

1. Subtract equations:

2. Solve x:

$\begin{gathered} 22x=66 \\ \frac{22}{22}x=\frac{66}{22} \\ \\ x=3 \end{gathered}$

3. Use the value of x=3 to solve y:

$\begin{gathered} 25x+16y=203 \\ 25(3)+16y=203 \\ 75+16y=203 \\ 75-75+16y=203-75 \\ 16y=128 \\ \frac{16}{16}y=\frac{128}{16} \\ \\ y=8 \end{gathered}$

Then, each small candleholder holds 3 candles, and each large one holds 8 candles