Adormitory manager buys 38 bed sheets and 61 towels for $791.50. the manager get another 54 bed sheets and 50 towels for $923 from the same store. what is the cost of one bed sheet and one towel?

Given:
1st purchase: 38 bed sheets and 61 towels for $791.50
2nd purchase: 54 bed sheets and 50 towels for $923

Let x = bed sheets ; y = towels

38x + 61y = 791.50
54x + 50y = 923.00

Find the value of y:

50y = 923.00 - 54x
y = 923/50 - 54x/50
y =  18.46 - 1.08x

Substitute y to find the value of x.
38x + 61y = 791.50
38x + 61(18.46 - 1.08x) = 791.50
38x + 1126.06 - 65.88x = 791.50
38x - 65.88x = 791.50 - 1126.06
- 27.88x =  -334.56
x = -334.56/ -27.88
x = 12

Find the value of y using the value of x.
y = 18.46 - (1.08x)
y = 18.46 - (1.08*12)
y = 18.46 - 12.96
y = 5.5

Each bed sheet costs $12 and each towel costs $5.50

To check:
38x + 61y = 791.50
38(12) + 61(5.5) = 791.50
456 + 335.5 = 791.50
791.50 = 791.50

54x + 50y = 923.00
54(12) + 50(5.5) = 923
648 + 275 = 923
923 = 923