The Physical Education Deparment sells t-shirts for $12 and shorts for $8. One month, they sold 77 total items for $780 in total. How many t-shirts did they sell?
Let T be the number of T-shirts sold and S be the number of shorts.
T + S = 77
12 T + 8 S = 780
Solve the two simulatneous equations.
12T + 12S = 924
4S = 144
S = 36
T = 41
41
To solve this problem, we can set up a system of equations. Let's call the number of t-shirts sold "t" and the number of shorts sold "s". From the given information, we have two equations:
Equation 1: The total number of items sold is 77: t + s = 77
Equation 2: The total amount earned is $780: 12t + 8s = 780
To find the number of t-shirts sold, we need to solve this system of equations.
Let's solve the system using the method of substitution. We can solve Equation 1 for "s" and substitute it into Equation 2:
Equation 1: t + s = 77 --> s = 77 - t
Substituting s in Equation 2:
12t + 8(77 - t) = 780
Now, we simplify and solve for t:
12t + 616 - 8t = 780
4t + 616 = 780
4t = 780 - 616
4t = 164
t = 164 / 4
t = 41
Therefore, the Physical Education Department sold 41 t-shirts.