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 equal small snack packs and Y equal large snack packs.
Part B- How many small snack packs did the snack bar sell? Use the elimination method to solve.
Part A:
The total number of snack packs sold is 60, so we can write one equation as:
X + Y = 60
The total revenue from selling small snack packs is $3*X, and the total revenue from selling large snack packs is $5*Y. The total revenue from selling all snack packs is $220, so we can write another equation as:
3*X + 5*Y = 220
Part B:
To solve the system of equations using the elimination method, we can multiply the first equation by 3:
3X + 3Y = 180
Then we can subtract this new equation from the second equation:
3*X + 5*Y - (3*X + 3*Y) = 220 - 180
2*Y = 40
Y = 20
So, the snack bar sold 20 large snack packs.