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

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

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 = (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.