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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?

At a historical landmark, candles are used to simulate an authentic atmosphere. A-example-1
User Alexander Sysoev
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1 Answer

9 votes
9 votes

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 \\ (22)/(22)x=(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 \\ (16)/(16)y=(128)/(16) \\ \\ y=8 \end{gathered}

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

At a historical landmark, candles are used to simulate an authentic atmosphere. A-example-1
User Ijaz Ahmad
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