(1) A business shipped 108 packages one day. Customers are charged $3.50 for each standard-delivery package and $7.50 for each express-delivery package. Total shipping charges for the day were $506.00. How many of each kind of package were shipped?

Question

Standard:

Express:

(2) A department store sold 41 shirts one day. All short-sleeved shirts cost $12.00 each and all long-sleeved shirts cost $17.00 each. Total receipts for the day were $582.00. How many of each kind of shirt were sold?

Short Sleeve:

Long Sleeve:

Answer 1

x+y=108
3.5x+7.5y=506

1st eq * 3.5 =
3.5x+3.5y = 378
subtract from second equation
4y = 128
y=32
x=76 (32+y=108 | 108-32 = 76)

Answer 2

#2 done the same way as the first

x+y = 41 ---#1
12x + 17y = 582 ---> #2

#1 times 12
12x + 12y = 492
12x + 17y = 582
subtract them:
5y = 90
y = 18
then x = 23

23 short-sleeved and 18 long-sleeved shirts