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 5 large candle holders, using a total of 64 candles. On the west side, he replaced the candles in 22 small candle holders and 20 large candle holders, for a total of 248 candles. How many candles does each candle holder hold? Each small candleholder holds _____ candles, and each large one holds _____ candles.

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  5 large candle holders, using a total of 64 candles. On the west side, he replaced the candles in 22 small candle holders and  20 large candle holders, for a total of 248 candles. How many candles does each candle holder hold?  Each small candleholder holds _____ candles, and each large one holds _____ candles.

Bytelearn · Accepted Answer

Define variables: Define the variables for the number of candles each type of candle holder can hold. Let x be the number of candles a small candle holder holds, and y be the number of candles a large candle holder holds.Write equations: Write the system of equations based on the given information. For the east side: 6 small holders and 5 large holders use 64 candles. 6x + 5y = 64 For the west side: 22 small holders and 20 large holders use 248 candles. 22x + 20y = 248Multiply and add: Multiply the first equation by -4 to align the coefficients of y for elimination. -4(6x + 5y) = -4(64) -24x - 20y = -256Eliminate y: Add the new equation from Step 3 to the second equation to eliminate y. (-24x - 20y) + (22x + 20y) = -256 + 248 -24x + 22x - 20y + 20y = -256 + 248 -2x = -8Solve for x: Solve for x. -2x = -8 x = -8 / -2 x = 4Substitute and solve for y: Substitute the value of x into one of the original equations to solve for y. 6x + 5y = 64 6(4) + 5y = 64 24 + 5y = 64 5y = 64 - 24 5y = 40 y = 40 / 5 y = 8Write final answer: Write the final answer. Each small candleholder holds 4 candles, and each large one holds 8 candles.

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