Question

write a system of equations to describe the situation below, solve using elimination, 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 6 small candle holders and 3 large candle holders, using a total of 36 candles. on the west side, he replaced the candles in 4 small candle holders and 6 large candle holders, for a total of 48 candles. how many candles does each candle holder hold? each small candleholder holds 　 candles, and each large one holds 　 candles.

Explanation:

Step1: Define Variables

Let \( x \) be the number of candles in a small candleholder, and \( y \) be the number in a large one.

Step2: Set Up Equations

From the east side: \( 6x + 3y = 36 \) (Equation 1)
From the west side: \( 4x + 6y = 48 \) (Equation 2)

Step3: Simplify Equations

Simplify Equation 1 by dividing by 3: \( 2x + y = 12 \) → \( y = 12 - 2x \) (Equation 1a)
Simplify Equation 2 by dividing by 2: \( 2x + 3y = 24 \) (Equation 2a)

Step4: Substitute \( y \) into Equation 2a

Substitute \( y = 12 - 2x \) into \( 2x + 3y = 24 \):
\( 2x + 3(12 - 2x) = 24 \)
\( 2x + 36 - 6x = 24 \)
\( -4x = -12 \)
\( x = 3 \)

Step5: Find \( y \)

Substitute \( x = 3 \) into Equation 1a: \( y = 12 - 2(3) = 6 \)

Answer:

Each small candleholder holds 3 candles, and each large one holds 6 candles.