Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ 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 $7$ small candle holders and $3$ large candle holders, using a total of $45$ candles. On the west side, he replaced the candles in $19$ small candle holders and $19$ large candle holders, for a total of $209$ candles. How many candles does each candle holder hold? $\newline$ Each small candleholder holds $\_$ candles, and each large one holds $\_$ candles.

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Solve a system of equations using elimination: word problems

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

\newline

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

7

small candle holders and

3

large candle holders, using a total of

45

candles. On the west side, he replaced the candles in

19

small candle holders and

19

large candle holders, for a total of

209

candles. How many candles does each candle holder hold?

\newline

Each small candleholder holds

\_

candles, and each large one holds

\_

candles.

Equation $1$ : Let's denote the number of candles a small candle holder holds as $s$ and the number of candles a large candle holder holds as $l$ . The volunteer replaced candles in $7$ small candle holders and $3$ large candle holders on the east side, using a total of $45$ candles. This gives us the equation $7s + 3l = 45$ .
Equation $2$ : On the west side, the volunteer replaced the candles in $19$ small candle holders and $19$ large candle holders, for a total of $209$ candles. This gives us the equation $19s + 19l = 209$ .
Eliminate Variable: We now have a system of two equations. We need to eliminate one of the variables, $s$ or $l$ . We choose to eliminate $l$ because its coefficients are the same in both equations. $\newline$ Step $4$ : To eliminate $l$ , we can subtract the first equation from the second equation. This gives us $19s + 19l - (7s + 3l) = 209 - 45$ . Simplifying this, we get $12s + 16l = 164$ .