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 3 small candle holders and 7 large candle holders, using a total of 65 candles. On the west side, he replaced the candles in 20 small candle holders and 7 large candle holders, for a total of 116 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 3 small candle holders and  7 large candle holders, using a total of 65 candles. On the west side, he replaced the candles in 20 small candle holders and  7 large candle holders, for a total of 116 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 size of candle holder holds. Let x be the number of candles a small candle holder holds. Let 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: 3x + 7y = 65 For the west side: 20x + 7y = 116Eliminate variable: Decide which variable to eliminate. We can eliminate y because it has the same coefficient in both equations.Subtract equations: Subtract the first equation from the second to eliminate y. (20x + 7y) - (3x + 7y) = 116 - 65 20x + 7y - 3x - 7y = 116 - 65 17x = 51Solve for x: Solve for x. 17x = 51 x = 51 / 17 x = 3Substitute x: Substitute x back into one of the original equations to solve for y. Using the first equation: 3x + 7y = 65 3(3) + 7y = 65 9 + 7y = 65 7y = 65 - 9 7y = 56 y = 56 / 7 y = 8Final answer: Write the final answer. Each small candleholder holds 3 candles, and each large one holds 8 candles.

Full solution

More problems from Solve a system of equations using elimination: word problems

Related topics