as a reward for passing the chapter 9 tex, Mrs. Pena purchased fun dips and reeses cups for her students. each fin dip cost $1.50 and each reeses cup costs $2.25. If she spent a total of $52.50 for 29 pieces of candy, how many of each tyoe of candy did she buy?

If each Fun Dips cost 1.5 dollars and Reese's for 2.25 and Mrs. Pena spent $52.50 dollars worth of Dips and Reese's then an equation representing this looks like this,

[tex]1.5d+2.25r=52.50[/tex].

If she bought 29 candies consisting of Reese's and Fun Dip then and equation can be written as,

[tex]d+r=29[/tex] ([tex]\star[/tex]).

Evaluating the System

Now having our system ready, we can rearrange the last equation in terms of r (or in terms of d) and substitute the d value in the first equation to find r's value before finding d!

[tex]d=29-r[/tex] ([tex]\star[/tex])

[tex]1.5(29-r)+2.25r=52.50[/tex] (replace d with [tex]\star[/tex])

[tex]43.5-1.5r+2.25r=52.50[/tex] (distribute the 1.5)

[tex]43.5+0.75r=52.50[/tex] (combine all like terms)

[tex]0.75r=9[/tex] (subtract 43.5 both sides)

[tex]r=12[/tex] (divide both sides by 0.75).

We plug back the now known r value into either equation but, as a short cut, we choose the [tex]d+r=29[/tex] equation for simplicity.

[tex]d+12=29\\d=29-12=17[/tex].