Question

concession stand sales
your team has been requested to help with the concession stand. the concession stand sells candy bars for $2 and bags of chips for $3. one day, the stand sold 8 more candy bars than chips and made $156.

a. create a model to represent the total amount of money earned based on the number of candy bars and chips sold.

b. create a model to represent the number of candy bars sold based on the number of chips sold.

c. use your models to determine the number of candy bars and chips sold at the game that day.

Explanation:

Step1: Define variables

Let $c$ = number of chips sold, $y$ = number of candy bars sold, $T$ = total money earned.

Step2: Model total earnings

Total revenue = (candy bar revenue) + (chip revenue)
$2y + 3c = 156$

Step3: Model candy bar quantity

Candy bars = chips + 8
$y = c + 8$

Step4: Substitute and solve for $c$

Substitute $y = c + 8$ into earnings equation:
$2(c + 8) + 3c = 156$
$2c + 16 + 3c = 156$
$5c + 16 = 156$
$5c = 156 - 16 = 140$
$c = \frac{140}{5} = 28$

Step5: Solve for $y$

Substitute $c=28$ into $y = c + 8$:
$y = 28 + 8 = 36$

Answer:

a. $2y + 3c = 156$
b. $y = c + 8$
c. Number of candy bars sold: 36; Number of chips sold: 28