Question

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 24 small candle holders and 3 large candle holders, using a total of 87 candles. On the west side, he replaced the candles in 14 small candle holders and 7 large candle holders, for a total of 77 candles. How many candles does each candle holder hold?
Each small candleholder holds ____ candles, and each large one holds ____ candles

Answer 1

Answer:

Each small candleholder holds 3 candles, and each large one holds 5 candles.

Step-by-step explanation:

This question can be solved by a system of equations.

I am going to say that:

x is the number of candles that a small candleholder holds.

y is the number of candles that a large candleholder holds.

24 small candle holders and 3 large candle holders, using a total of 87 candles.

This means that

$24x + 3y = 87$

Simplifying by 3

$8x + y = 29$

$y = 29 - 8x$

14 small candle holders and 7 large candle holders, for a total of 77 candles.

This means that $14x + 7y = 77$

Simplifying by 7

$2x + y = 11$

$y = 11 - 2x$

Since $y = 29 - 8x$

$11 - 2x = 29 - 8x$

$6x = 18$

$x = \frac{18}{6}$

$x = 3$

$y = 29 - 8x = 29 - 8*3 = 29 - 24 = 5$

Each small candleholder holds 3 candles, and each large one holds 5 candles.