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 system of equations that represents the scenario is:
x + y = 60 (equation 1)
3x + 5y = 220 (equation 2)
Part B:
To solve for the number of small snack packs sold (x), we can use the elimination method.
Step 1: Multiply equation 1 by -3 to eliminate the x term.
-3(x + y) = -3(60)
-3x - 3y = -180 (equation 3)
Step 2: Add equation 3 to equation 2 to eliminate the x term.
(-3x - 3y) + (3x + 5y) = -180 + 220
2y = 40
Step 3: Divide both sides of the equation by 2.
2y/2 = 40/2
y = 20
Step 4: Substitute the value of y into equation 1 to solve for x.
x + 20 = 60
x = 60 - 20
x = 40
So, the snack bar sold 40 small snack packs.