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

Answer:

The number of candles will hold 2 candles

And large candle holder will hold 6 candles.

Step-by-step explanation:

Let the number of candles  small candle holder have x

And the number of candles large candle holder have y

So, according to the information given in the question:

17 small candle holders means 17 x

and 2 large candle holders means 2y

using a total of 46 candles means $17x+2y=46$     (1)

Similarly, 8 small candle holders and 2 large candle holders, for a total of 28 candles gives:

$8x+2y=28$      (2)

We will solve equation (1) and (2) by elimination method:

Subtractijng the two equations we get:

$9x=18$

$\Rightarrow x=2$

Substitute x=2 in equation(2) we get:$8(2)+2y=28$

$2y=12$

$\Rightarrow y=6$

So, the number of candles will hold 2 candles

And large candle holder will hold 6 candles.