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. SOLVE FOR X, SOLVE FOR HOW MANY SMALL PACKS THE SNACK BAR SOLD.
The system of equations that represents the scenario is:
x + y = 60 (equation 1) - represents the total number of snack packs sold
3x + 5y = 220 (equation 2) - represents the total amount of money made from the snack packs sold
To solve using the elimination method, we will multiply equation 1 by 3 to make the coefficients of x in both equations the same:
3(x + y) = 3(60)
3x + 3y = 180 (equation 3)
Now we can subtract equation 3 from equation 2 to eliminate x:
(3x + 5y) - (3x + 3y) = 220 - 180
2y = 40
Finally, we divide both sides of the equation by 2 to solve for y, the number of large snack packs sold:
2y/2 = 40/2
y = 20
Therefore, the snack bar sold 20 large snack packs.
Now, we can substitute the value of y into equation 1 to solve for x:
x + 20 = 60
x = 60 - 20
x = 40
Therefore, the snack bar sold 40 small snack packs.