A concession stand sells apple cider for $3.35 a cup and donuts for $2.45 each, on Saturday the stand sold 126 items and made $362.70 how many cups of apple cider did the stand sell

The number of cups of apple cider sold was 60 cups

Step-by-step explanation:

We will develop equations to solve this problem.

Let a = price for a cup of apple cider in dollars

Let b = price for a donut in dollars

Let x = number for cups of apple cider sold

Let y = number of donuts sold

Let z = number of items sold on the day = 126 items

Let v = total money made = $362.70

Lets write two equations. One in terms of the amount of items sold of cups of apple cider and donuts, and one in terms of how much money was made for selling cups of apple cider and donuts.

z = x + y

x = z - y (1)

v = ax + by (2)

we substitute equation 1 in to equation 2

v = a (z-y) + by = az - ay + by = az + y (b-a)

solve for y

y = (v-az) / (b-a) = (362.70 - 3.35*126) / (2.45-3.35) = 66 donuts were sold

therefore x = z-y = 126-66 = 60 cups of apple cider were sold

52 cups.

3.35 times 52 equals 174.20

2.45 times 77 equals 188.60

So 52 cups of apple cider were sold in total.