A snack bar sells two sizes of snack packs. A large snack pack is $5 and a small pack is $3. In one day, the snack bar sold 60 packs for a total of $220. Write a system of equations that represents the scenario above. Let x = small packs and y = large snack packs. How many small packs did the snack bar sell? Use the elimination method to solve.
We can set up a system of equations to represent the scenario:
x = number of small packs
y = number of large packs
The total number of packs sold is 60, so we have the equation:
x + y = 60
The total amount of money made from small packs is $3 times the number of small packs, so we have the equation:
3x = amount made from small packs
The total amount of money made from large packs is $5 times the number of large packs, so we have the equation:
5y = amount made from large packs
The total amount made from both types of packs is $220, so we have the equation:
3x + 5y = 220
To solve this system of equations using the elimination method, we can multiply the first equation by 3 to make the coefficients of x in both equations the same:
3(x + y) = 3(60)
3x + 3y = 180
Now we have the two equations:
3x + 3y = 180 (equation 1)
3x + 5y = 220 (equation 2)
We can subtract equation 1 from equation 2 to eliminate the x term:
(3x + 5y) - (3x + 3y) = 220 - 180
2y = 40
Dividing both sides of the equation by 2, we get:
y = 20
Therefore, the snack bar sold 20 large packs.