Chapter 5.1, Problem 28E

To determine

To find: the number of candles sold

Answer to Problem 28E

Thus, 12 small candles and 16 large candles should be sold.

Explanation of Solution

Given:

There are 28 candles sold for $144

Calculation:

Let $x$ be the number of small candles and $l$ be the number of large candles

  $\begin{array}{r}\hfill x+y=28\\ \hfill 4x+6y=144\end{array}$

Rearranging,

  $\begin{array}{l}y=28-x\hfill \\ y=24-\frac{2}{3}x\hfill \end{array}$

The first equation is plotted in red colour and the second equation in blue colour.

  

In graph, it seems that (12,16) is solution of system of equations. Check if it is indeed the solution.

  $\begin{array}{l}x+y=28\\ 12+16=28\\ 28=28\\ 4x+6y=144\\ 4(12)+6(16)=144\\ 48+96=144\\ 144=144\end{array}$

As the point satisfies both equations, it is solution of system of equations.

Thus, 12 small candles and 16 large candles should be sold.

Conclusion:

Thus, 12 small candles and 16 large candles should be sold.