Answer :
Answer:
She bought 17 fun dips and 12 Reese's cups.
Step-by-step explanation:
A system of equations can be produces in terms of Fun Dips, d and Reese's cups, r.
Turning Words into Equations
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].
