Exercise 28 Page 240

We are told that we sold total of $28$ candles. If we let $s$ be the number of small candles sold and $\ell$ be the number of large candles sold, we can write an equation to represent the total number of candles. We will rearrange this equation by isolating one of the variables $\ell$ to use it later easily. We also know that a large candle costs $\$6$ and a small candle costs $\$4.$ With that information we will express how much we collected in terms of $s$ and $\ell .$

Verbal expression	Algebraic expression
Price per large candle	$6$
Number of large candles sold	$\ell$
Money collected from selling large candles	$6\ell$
Price per small candle	$4$
Number of small candles sold	$s$
Money collected from selling small candles	$4s$
Total amount of money collected	$6\ell +4s$

Since we collected $\$144,$ let's build an equation to express the total amount of money with the number of the candles. Now, we will rearrange this equation by isolating $\ell$ because it will help us graph this equation. Now that we have both equations in slope-intercept form, we can plot them and find the point of interception. From the graph we can see that point $(12,16)$ is the solution. However, we should check the point by substituting it into the equations. Let's start with the first one. Now, we will check the second one. Since both equations hold true, point $(12,16)$ is a solution. This means that you sold $12$ small candles and $16$ large candles.