Noah works at a concession stand selling bags of popcorn and cans of soda. A bag of popcorn costs $2.50 and a can of soda costs $1.50. One night, he notices that he sold a total of 300 items and collected a total of $522. Determine the system of equations that could be used to solve this problem, where x represents the number of bags of popcorn sold and y represents the number of cans of soda sold

Set up 2 equations:

Total items sold: x + y = 300

This gets rewritten as x = 300-y

The second equation is for total amount made:

2.50x + 1.50y = 522

Replace x in the 2nd equation with the value of x from the first one:

2.50(300-y) + 1.50y = 522

Simplify:

750 - 2.50y + 1.50y = 522

Combine like terms:

750 - y = 522

Subtract 750 from both sides:

-y = -228

Divide both sides by -1 ( to make y positive)

y = 228

Now replace y in the first equation to solve for x:

x+ 228 = 300

Subtract 228 from both sides:

x = 72

He sold 72 bags of popcorn and 228 sodas.