Question

Algebradations usingWrite a system of equations to describe the situation below, solve using elimination, and fill inthe blanks.At a historical landmark, candles are used to simulate an authentic at mosphere. A volunteeris currently putting new candles in the candle holders. On the east side, he replaced candlesin 22 small candle holders and 4 large candle holders, using a total of 64 candles. On thewest side, he replaced the candles in 21 small candle holders and 21 large candle holders, fora total of 147 candles. How many candles does each candle holder hold?

Answer 1

Answer:

A small candle holder holds 2 candles

A large candle holder holds 5 candles

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:

$\begin{gathered} 18s\text{ = 36} \\ s\text{ = }\frac{36}{18}\text{ = 2} \end{gathered}$

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:

$\begin{gathered} 18l\text{ = 90} \\ l\text{ = }\frac{90}{18} \\ l\text{ = 5} \end{gathered}$