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 17 small candle holders and 2 large candle holders, using a total of 46 candles. On the west side, he replaced the candles in 8 small candle holders and 2 large candle holders, for a total of 28 candles. How many candles does each candle holder hold? Each small candleholder holds candles, and each large one holds candles. Submit

Answer 1

To solve this problem, we can set up a system of equations and use the method of elimination to find the solution. Each small candle holder holds 1 candle, and each large candle holder holds 8 candles.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's denote the number of candles in each small candle holder as x, and the number of candles in each large candle holder as y.

The information given can be translated into the following system of equations:

1. 17x + 2y = 46 (for the east side)
2. 8x + 2y = 28 (for the west side)

Using the method of elimination, we can multiply equation 2 by 2 and subtract it from equation 1 to eliminate y:

1. 17x + 2y = 46
2. 16x + 4y = 56
3. -16x - 2y = -28
4. ---------------------
5. 1x + 2y = 18

Now we have a new equation, 1x + 2y = 18, which we can solve using any method of our choice. For convenience, we can multiply it by 2 to eliminate the fraction:

1. 2x + 4y = 36
2. 1x + 2y = 18

Subtracting equation 2 from equation 1, we get:

1. 2x + 4y - (1x + 2y) = 36 - 18
2. 1x + 2y = 18
3. ---------------------
4. 1x + 2y = 18

So, the solution is x = 1 and y = 8. Each small candle holder holds 1 candle, and each large candle holder holds 8 candles.