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?
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.
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,
\(1.5d+2.25r=52.50\).
If she bought 29 candies consisting of Reese's and Fun Dip then and equation can be written as,
\(d+r=29\) (\(\star\)).
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!
\(d=29-r\) (\(\star\))
\(1.5(29-r)+2.25r=52.50\) (replace d with \(\star\))
\(43.5-1.5r+2.25r=52.50\) (distribute the 1.5)
\(43.5+0.75r=52.50\) (combine all like terms)
\(0.75r=9\) (subtract 43.5 both sides)
\(r=12\) (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 \(d+r=29\) equation for simplicity.
\(d+12=29\\d=29-12=17\).