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

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joaobezerra joaobezerra · Answer 1 · 2021-03-02T01:16:07+01:00

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

[tex]24x + 3y = 87[/tex]

Simplifying by 3

[tex]8x + y = 29[/tex]

[tex]y = 29 - 8x[/tex]

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

This means that [tex]14x + 7y = 77[/tex]

Simplifying by 7

[tex]2x + y = 11[/tex]

[tex]y = 11 - 2x[/tex]

Since [tex]y = 29 - 8x[/tex]

[tex]11 - 2x = 29 - 8x[/tex]

[tex]6x = 18[/tex]

[tex]x = \frac{18}{6}[/tex]

[tex]x = 3[/tex]

[tex]y = 29 - 8x = 29 - 8*3 = 29 - 24 = 5[/tex]

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