Ethan sells $e$ candy bars for $\$ 2.50$ apiece and Chloe sells $c$ candy bars for $\$ 2.00$ apiece to raise money for a school trip. Ethan sold $15$ fewer candy bars than Chloe, but he also got a $\$ 6.00$ donation. If Chloe and Ethan raised the same amount of money, which of the following systems could be used to find how many candy bars each sold? $\newline$ Choose $1$ answer: $\newline$ (A) $2 c=2.5 e+6$ $\newline$ $c=e-15$ $\newline$ (B) $2 c=2.5 e+6$ $\newline$ $e=c-15$ $\newline$ (C) $2 c+6=2.5 e$ $\newline$ $c=e-15$ $\newline$ (D) $2 c+6=2.5 e$ $\newline$ $e=c-15$

Full solution

Q. Ethan sells

e

candy bars for

\$ 2.50

apiece and Chloe sells

c

candy bars for

\$ 2.00

apiece to raise money for a school trip. Ethan sold

15

fewer candy bars than Chloe, but he also got a

\$ 6.00

donation. If Chloe and Ethan raised the same amount of money, which of the following systems could be used to find how many candy bars each sold?

\newline

Choose

1

answer:

\newline

(A)

2 c=2.5 e+6

\newline

c=e-15

\newline

(B)

2 c=2.5 e+6

\newline

e=c-15

\newline

(C)

2 c+6=2.5 e

\newline

c=e-15

\newline

(D)

2 c+6=2.5 e

\newline

e=c-15

Set Up Equations: Step $1$ : Let's set up the equations based on the information given. Ethan's total money raised is from selling candy bars at $\$2.50$ each plus a $\$6.00$ donation. Chloe's total money raised is from selling candy bars at $\$2.00$ each. They raised the same amount of money, so we can set their equations equal to each other.
Calculate Candy Bars: Step $2$ : Ethan sold $15$ fewer candy bars than Chloe, so if Chloe sold $c$ candy bars, then Ethan sold $c - 15$ candy bars.
Write Ethan's Equation: Step $3$ : Now let's write the equation for the money Ethan raised: $2.50(e) + 6$ . Since $e = c - 15$ , we can substitute to get $2.50(c - 15) + 6$ .
Write Chloe's Equation: Step $4$ : Write the equation for the money Chloe raised: $2.00(c)$ .
Set Equations Equal: Step $5$ : Since they raised the same amount of money, we can set the equations equal to each other: $2.50(c - 15) + 6 = 2.00(c)$ .
Simplify Equation: Step $6$ : Now we need to find which answer choice matches our equation. Let's simplify our equation first: $2.5c - 37.5 + 6 = 2c$ .
Final Simplification: Step $7$ : Simplify further by adding $37.5$ to both sides: $2.5c - 31.5 = 2c$ .