A snack bar sells two sizes of snack packs. A large snack pack is $5, and a small snack pack is $3. In one day, the snack bar sold 60 snack packs for a total of $220. Part A Write a system of equations that represents the scenario above. Let x = small snack packs and y = large snack packs. Part B How many small snack packs did the snack bar sell? Use the Elimination Method to solve. You must show work.
Part A:
The total number of snack packs sold is 60, so we can write the equation:
x + y = 60
The total amount of money made from the small snack packs is $3 times the number of small snack packs (x), and the total amount of money made from the large snack packs is $5 times the number of large snack packs (y).
So we can write the equation:
3x + 5y = 220
Part B:
To solve the system of equations using the Elimination Method, we can multiply the first equation by 3 to make the coefficients of x in both equations equal:
3(x + y) = 3(60)
3x + 3y = 180
Now we can subtract this new equation from the second equation to eliminate x:
3x + 5y - (3x + 3y) = 220 - 180
2y = 40
y = 40/2
y = 20
Now we can substitute the value of y in the first equation to find x:
x + 20 = 60
x = 60 - 20
x = 40
Therefore, the snack bar sold 40 small snack packs.