1 Answer

Orangutan · Answer 1 · 2023-06-27T05:16:42+0000

Answer:

A small candle holder holds 2 candles

A large candle holder holds 5 candles

Step-by-step explanation:

Here, we want to set up a system of linear equations which we will proceed to solve simultaneously by the elimination method

Let the number of small candles held be s and the number of large candles held be l

Let us start with the east side:

there were 22 small candle holders and 4 large candle holders to give a total of 64 candles

Mathematically:

$\begin{gathered} 22(s)\text{ + 4\lparen l\rparen = 64} \\ 22s\text{ + 4l = 64} \end{gathered}$

For the west side:

there were 21 small candle holders and 21 large candle holders to give a total of 147 candles:

$\begin{gathered} 21(s)\text{ + 21\lparen l\rparen = 147} \\ s\text{ + l = 7} \end{gathered}$

The two equations we are to solve simultaneously by elimination are:

$\begin{gathered} 22s\text{ + 4l = 64} \\ s\text{ + l = 7} \end{gathered}$

Multiply the second equation by 4 and the first by 1

We have that as:

$\begin{gathered} 4l\text{ + 22s = 64} \\ 4l\text{ + 4s = 28} \end{gathered}$

Subtract equation ii from i:

$\begin{gathered} 18s\text{ = 36} \\ s\text{ = }(36)/(18)\text{ = 2} \end{gathered}$

For l, we multiply the first equation by 1 and the second by 22

We have that as:

$\begin{gathered} 22s\text{ + 4l = 64} \\ 22s\text{ + 22l = 154} \end{gathered}$

Subtract the first equation from the second:

$\begin{gathered} 18l\text{ = 90} \\ l\text{ = }(90)/(18) \\ l\text{ = 5} \end{gathered}$

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